# How do you solve the equation 2x^2+10x=-17 by completing the square?

Mar 3, 2018

color(red)(x =  color(green)(-(1/2)(5-3i), (-1/2)(5+3i)

#### Explanation:

$2 {x}^{2} + 10 x = - 17$

Divide by 2 on both sides. ${x}^{2} + 5 x = - \frac{17}{2}$

Rewrite the (xy term as multiple of 2

${x}^{2} + \left(2 \cdot x \cdot \left(\frac{5}{2}\right)\right) = - \frac{17}{2}$

Complete the square on L H S by adding ${\left(\frac{5}{2}\right)}^{2}$ to both sides.

x^2 + (2*(5/2) x+ (5/2)^2 = -17 / 2 + (5/2)^2 = -9/4

(x+5/2)^2 = (sqrt(-9/4)^2 = (i * (3/2)^2

$x + \frac{5}{2} = \pm \left(\frac{3}{2}\right) i$

color(red)(x ) = color(blue)(-5/2 + 3/2i, -5/2 -3/2i or color(green)(-(1/2)(5-3i), (-1/2)(5+3i)#