(x-4)(x-10)=-9

2 min read Jun 17, 2024

Solving the Quadratic Equation: (x-4)(x-10) = -9

This article will guide you through the steps to solve the quadratic equation (x-4)(x-10) = -9.

First, we expand the left side of the equation by multiplying the terms:

(x-4)(x-10) = x² - 10x - 4x + 40

Simplifying, we get:

x² - 14x + 40 = -9

Next, we move the constant term (-9) to the left side of the equation:

x² - 14x + 40 + 9 = 0

This gives us:

x² - 14x + 49 = 0

Now, we factor the quadratic equation. We need to find two numbers that add up to -14 and multiply to 49. These numbers are -7 and -7.

Therefore, we can factor the equation as:

(x - 7)(x - 7) = 0

To solve for x, we set each factor equal to zero:

x - 7 = 0 or x - 7 = 0

Solving for x in both cases gives us:

x = 7

The solution to the quadratic equation (x-4)(x-10) = -9 is x = 7. This means that the equation is true only when x is equal to 7.