solve and check (x - 5)(x - 10) = -4

Question

how do you solve the problem (x - 5)(x - 10) = -4.

Answer 1

(x - 5)(x - 10) = -4

x(x) - x (10) - 5(x) - 5(-10) = -4

x^2 - 10x - 5x + 50 = -4

x^2 - 15x + 50 = -4

Add 4 to each side.

x^2 -15x + 54 = 0

x^2 - 9x - 6x + 54 = 0

x(x - 9) - 6(x - 9) = 0

(x - 9)(x - 6) = 0

x - 6 = 0

Add 6 to each side.

x = 6.

And x - 9 = 0

Add 9 to each side.

x = 9.

Solution x = 9 and 6.

Check:

For x = 6

(6 - 5)(6 - 10) = -4

1(-4) = -4

-4 = -4

For x = 9

(9 - 5)(9 - 10) = -4

4(-1) = -4

-4 = -4.