Question

Solve for x in the equation x2-14x+31=63?

Answer 1

Value of x are 16 and -2

Explanation:

Solve for x in the equation:

`x^2-14x+31 = 63`

Subtract 63 from both sides we have;

`x^2-14x-32=0`

To factor this equation as:

`x^2-16x+2x-32=0`

⇒
`x(x-16)+2(x-16)=0`

Take (x-16) common we have;

⇒
`(x-16)(x+2)=0`

By zero product property we have;

x-16 = 0 or x+2 = 0

⇒x = 16 or x = -2

Therefore, the value of x are: 16 and -2

Answer 2

x² -14x +31 = 63
x² -14x +49 = 81 . . . . . add 18 to complete the square
(x -7)² = 81
x -7 = ±√81 = ±9
x = 7 ±9

x = -2 or 16