How to solve x2 4x 4?

To solve the equation x^2 + 4x + 4, you need to factorize the expression. First, observe that the given expression is a quadratic equation in the form of ax^2 + bx + c, where a = 1, b = 4, and c = 4.

Next, you need to find two numbers whose product is equal to ac (in this case, 1 * 4 = 4) and whose sum is equal to b (in this case, 4). Let's call these numbers p and q.

Since ac = 4 and p + q = 4, we can conclude that p = 2 and q = 2. Hence, we can rewrite the equation x^2 + 2x + 2x + 4 as (x^2 + 2x) + (2x + 4).

Now, we can factor out the common terms from each pair of parentheses:

(x^2 + 2x) + (2x + 4)

x(x + 2) + 2(x + 2)

(x + 2)(x + 2)

Finally, we can rewrite the equation in factored form as (x + 2)(x + 2). Since both parentheses are the same, we can simplify it further:

(x + 2)^2

Therefore, the solution to the equation x^2 + 4x + 4 is (x + 2)^2.

What are the factors of x2 4x 4?

What are the factors of x2 4x 4?

The given expression is a quadratic equation in the form of ax^2 + bx + c. In this case, the equation is x^2 + 4x + 4.

To find the factors of this quadratic equation, we need to identify two numbers that when multiplied together, give us the constant term (c) and when added together, give us the coefficient of x (b).

The constant term (c) in this equation is 4, and the coefficient of x (b) is also 4.

We can list all the factors of 4 to help us find the pairs of numbers that satisfy the given conditions. The factors of 4 are 1, 2, and 4.

Let's try these factors to see which combinations give us a sum of 4 and a product of 4:

Pair 1: 1 and 4

1 + 4 = 5 (not equal to 4)

1 × 4 = 4 (equal to 4)

This pair does not satisfy the conditions, so it is not a factor of the given equation.

Pair 2: 2 and 2

2 + 2 = 4 (equal to 4)

2 × 2 = 4 (equal to 4)

This pair satisfies the conditions and is a factor of the given equation.

Therefore, the factors of x^2 + 4x + 4 are (x + 2)(x + 2) or simply (x + 2)^2.

How to solve quadratic equation?

Solving a quadratic equation is a fundamental concept in mathematics. It involves finding the values of 'x' that satisfy the equation. Quadratic equations can be solved using different methods. Here, we will discuss a common approach called the Quadratic Formula.

The Quadratic Formula is expressed as: x = (-b ± √(b^2 - 4ac)) / (2a). This formula is derived from the standard form of a quadratic equation: ax^2 + bx + c = 0.

The first step in solving a quadratic equation is to identify the values of 'a', 'b', and 'c'. These coefficients can be obtained by comparing the given equation to the standard form. Once we have these values, we can substitute them in the Quadratic Formula to find the solutions for 'x'.

Let's consider an example: Solve the quadratic equation 3x^2 - 7x + 2 = 0.

Step 1: Identify the values of 'a', 'b', and 'c'.

In this case, 'a' = 3, 'b' = -7, and 'c' = 2.

Step 2: Substitute the values into the Quadratic Formula.

x = (-(-7) ± √((-7)^2 - 4(3)(2))) / (2(3))
x = (7 ± √(49 - 24)) / 6
x = (7 ± √25) / 6
x = (7 ± 5) / 6

Step 3: Simplify the solutions.

The solutions to the quadratic equation are obtained by evaluating the expressions inside the square root.

x = (7 + 5) / 6 = 12 / 6 = 2
x = (7 - 5) / 6 = 2 / 6 = 1/3

Hence, the solutions to the quadratic equation 3x^2 - 7x + 2 = 0 are x = 2 and x = 1/3.

Remember, there are other methods to solve quadratic equations, such as factoring or completing the square. However, the Quadratic Formula is a reliable and widely used approach.

In conclusion, solving quadratic equations involves using the Quadratic Formula to determine the values of 'x' that make the equation true. By substituting the coefficients of the quadratic equation into the formula, we can find the solutions. It is important to grasp this concept, as it is fundamental in various fields of mathematics and science.

What is the discriminant of x2 4x 4?

The discriminant of a quadratic equation in the form ax² + bx + c = 0 is calculated using the formula D = b² - 4ac. In this case, the quadratic equation is x² + 4x + 4 = 0, where a = 1, b = 4, and c = 4.

Therefore, the discriminant can be found as follows:

D = (4)² - 4(1)(4) = 16 - 16 = 0

The discriminant value helps determine the nature of the roots of a quadratic equation. If the discriminant is positive, the equation has two distinct real roots. If the discriminant is zero, the equation has one real root with a multiplicity of two. And if the discriminant is negative, the equation has two complex conjugate roots.

In this case, since the discriminant is equal to zero, the quadratic equation x² + 4x + 4 = 0 has one real root with a multiplicity of two. This means that the equation has a repeated root at x = -2.

The discriminant is an essential concept in quadratic equations as it provides valuable information about the nature of the roots, enabling us to understand the behavior of the equation graphically and algebraically.

How do you solve 4 quadratic equations?

Quadratic equations are second-degree polynomial equations in a single variable. They can be written in the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable. Solving quadratic equations involves finding the values of x that satisfy the equation.

There are several methods to solve quadratic equations. One of the most common methods is factoring. This method involves factoring the quadratic equation into two binomials and setting each binomial equal to zero. By solving these two equations, you can find the values of x.

Another method that can be used to solve quadratic equations is completing the square. This method involves manipulating the equation to create a perfect square trinomial. By taking the square root of both sides of the equation and isolating x, you can find the solutions of the quadratic equation.

The quadratic formula is another powerful tool to solve quadratic equations. The formula is derived by completing the square and can be stated as x = (-b +/- sqrt(b^2 - 4ac)) / (2a). By substituting the values of a, b, and c into the quadratic formula, you can calculate the values of x that satisfy the equation.

Lastly, graphing can also be used to solve quadratic equations. By graphing the quadratic equation on a coordinate plane, the x-intercepts of the graph represent the solutions to the equation. This method is useful for visualizing the solutions and understanding the behavior of the quadratic equation.

In conclusion, solving quadratic equations can be done using various methods such as factoring, completing the square, applying the quadratic formula, or graphing. Each method has its advantages and may be more appropriate depending on the specific equation and the desired level of accuracy. These techniques provide a systematic approach to finding the solutions of quadratic equations in a straightforward and efficient manner.