Question

Solve by factoring. Show all steps including the table and the "fractions" used to get the factors. No work = No credit.

x² - 2x = 15
x=-5 and -3
x= 5 and 3
x=-5 and 3
x= 5 and -3

Answer 1

To solve the quadratic equation x² - 2x = 15, we first rearrange it as an equation set to zero, then factor and solve for x, finding that the solutions are x = 5 and x = -3.

Step-by-step explanation:

To solve the equation x² - 2x = 15 by factoring, let's first move all terms to one side to set the equation equal to zero:

x² - 2x - 15 = 0

Next, we look for two numbers that multiply to -15 (the constant term) and add to -2 (the coefficient of the linear term). These numbers are -5 and 3. The equation can thus be factored as:

(x - 5)(x + 3) = 0

To find the values of x, we set each factor equal to zero:

• x - 5 = 0 → x = 5
• x + 3 = 0 → x = -3

Therefore, the solutions to the equation are x = 5 and x = -3.