7.5k views
0 votes
Please do number 12. Solve each equation by completing the square. Simplify all irrational and complex situations

Please do number 12. Solve each equation by completing the square. Simplify all irrational-example-1

1 Answer

4 votes

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}

User Quima
by
3.9k points