(x-9)%3D195.jpeg "(x-7)(x-9)=195")
Solving the Equation: (x-7)(x-9) = 195
This equation represents a quadratic equation, and we can solve it to find the possible values of x. Here's a step-by-step approach:
1. Expand the Left Side
First, we need to expand the left side of the equation by multiplying the two binomials:
(x-7)(x-9) = x² - 9x - 7x + 63
Simplifying this, we get:
x² - 16x + 63 = 195
2. Move the Constant Term
Now, we need to move the constant term to the right side of the equation:
x² - 16x = 195 - 63
This simplifies to:
x² - 16x = 132
3. Solve the Quadratic Equation
We can now solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula, which is:
x = [-b ± √(b² - 4ac)] / 2a
In this equation, a = 1, b = -16, and c = -132. Substituting these values into the formula, we get:
x = [16 ± √((-16)² - 4 * 1 * -132)] / (2 * 1)
Simplifying the equation further:
x = [16 ± √(256 + 528)] / 2
x = [16 ± √784] / 2
x = [16 ± 28] / 2
This gives us two possible solutions for x:
x₁ = (16 + 28) / 2 = 22
x₂ = (16 - 28) / 2 = -6
Therefore, the solutions to the equation (x-7)(x-9) = 195 are x = 22 and x = -6.