(x-4)%3D55.jpeg "(x-10)(x-4)=55")
Solving the Equation: (x-10)(x-4) = 55
This equation involves a quadratic expression and can be solved by following these steps:
1. Expand the Equation
First, expand the left side of the equation by multiplying the two binomials:
(x-10)(x-4) = x² - 14x + 40
Now the equation becomes:
x² - 14x + 40 = 55
2. Rearrange the Equation
Next, move the constant term from the right side to the left side to set the equation equal to zero:
x² - 14x + 40 - 55 = 0
This simplifies to:
x² - 14x - 15 = 0
3. Factor the Quadratic Expression
Now we need to factor the quadratic expression on the left side. We're looking for two numbers that add up to -14 and multiply to -15. These numbers are -15 and 1:
(x - 15)(x + 1) = 0
4. Solve for x
Finally, set each factor equal to zero and solve for x:
- x - 15 = 0 => x = 15
- x + 1 = 0 => x = -1
Solutions
Therefore, the solutions to the equation (x-10)(x-4) = 55 are:
x = 15 and x = -1