We know that (x+a)

2a = -16

a = -16/2 = -8

If we add a

x

x

(x-8)

Solution:

(x-8)

(x-8)

x - 8 = ±√49 (take the square root of both sides)

x = 8 ± 7 (add 8 to both sides)

x = {1, 15}

Check 1

We know the factors of a quadratic are (x-root1)(x-root2)

(x-1)(x-15) = x

Check 2

Try the roots one at a time.

(1)2 -16(1) +15 = 0 (x=1)

1 - 16 + 15 = 0 (yes)

(15)

15(15 - 16 + 1) = 0 (yes)

^{2}= x^{2}+ 2ax + a^{2}, so we know that a is half the coefficient of the x term.2a = -16

a = -16/2 = -8

If we add a

^{2}to both sides of the equation, we can complete the square.x

^{2}- 16x + 15 = 0x

^{2}- 16x + 64 + 15 = 64 (we have added 64 so we can complete the square)(x-8)

^{2}+ 15 = 64Solution:

(x-8)

^{2}= 64 - 15 (subtract 15 from both sides)(x-8)

^{2}= 49 (This may be the form you prefer for the equation with the square complete.)x - 8 = ±√49 (take the square root of both sides)

x = 8 ± 7 (add 8 to both sides)

x = {1, 15}

Check 1

We know the factors of a quadratic are (x-root1)(x-root2)

(x-1)(x-15) = x

^{2}-15x -1x +15 = x^{2}-16x +15 (original equation. This checks both roots at once.)Check 2

Try the roots one at a time.

(1)2 -16(1) +15 = 0 (x=1)

1 - 16 + 15 = 0 (yes)

(15)

^{2}- 16(15) + 15 = 0 (x=15)15(15 - 16 + 1) = 0 (yes)