Question

Please do number 12. Solve each equation by completing the square. Simplify all irrational and complex situations

Answer 1

12)

2x^2 - 20x + 89 = - 87

2x^2 - 20x = - 87 - 89

2x^2 - 20x = - 176

Dividing both sides of the equation by 2, we have

x^2 - 10x = - 88

We would add the square root of half the coefficient of x to both sides. We would add (- 5)^2 to both sides. We have

x^2 - 10x + (- 5)^2 = - 88 + (- 5)^2

(x - 5)^2 = - 88 + 25 = - 63

Taking square root of both sides, we have

`\begin{gathered} x\text{ - 5 = }\pm\sqrt[]{-\text{ 63}} \\ x\text{ = 5 }\pm\sqrt[]{-\text{ 63}} \\ x\text{ = 5 + 63i or x = 5 - 63i} \end{gathered}`