(x-10)(x-4)=55

2 min read Jun 17, 2024
(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

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