Solve for all values of xx by factoring.
x, squared, minus, 15, x, plus, 7, equals, minus, 6, x, minus, 1
x
2
−15x+7=
−6x−1
To solve for x by factoring, we want to set the equation equal to 0:
x^2 - 15x + 7 = -6x - 1
Moving everything to one side, we get:
x^2 - 9x + 8 = 0
Now, we can factor the quadratic equation:
(x - 8)(x - 1) = 0
Now, we can set each factor equal to 0 to solve for x:
x - 8 = 0
x = 8
x - 1 = 0
x = 1
Therefore, the solutions for x are x = 8 and x = 1.