The usual techniques are

1. Factoring

x

(x-13)(x+3) = 0 (39=3*13, factors that happen to differ by the required 10)

x = 13, x = -3

2. Completing the square

x

x

(x-5)

x-5 = ±8 (square root both sides)

x = 5±8 (add 5 to both sides)

x = {13, -3}

3. Quadratic formula (this is the same as jumping straight to the end of completing the square)

x

x = (-(-10) ±√((-10)

= (10 ±√(100 + 156))/2

= (10 ±√256)/2

= (10±16)/2

= 5±8

x = {13, -3}

1. Factoring

x

^{2}- 10x - 39 = 0(x-13)(x+3) = 0 (39=3*13, factors that happen to differ by the required 10)

x = 13, x = -3

2. Completing the square

x

^{2}- 10x - 39 = 0x

^{2}- 10x + 25 = 64 (add 64 to both sides)(x-5)

^{2}= 64 (show the square we have completed)x-5 = ±8 (square root both sides)

x = 5±8 (add 5 to both sides)

x = {13, -3}

3. Quadratic formula (this is the same as jumping straight to the end of completing the square)

x

^{2}- 10x - 39 = 0x = (-(-10) ±√((-10)

^{2}- 4(1)(-39)))/(2(1))= (10 ±√(100 + 156))/2

= (10 ±√256)/2

= (10±16)/2

= 5±8

x = {13, -3}