X^2+18x+71 = 0

Solve the quadratic equation by completing the square.

x = sqrt (10) - 9 or x = - 9 - sqrt (10)

Step-by-step explanation by completing the square:

Solve for x:

x^2 + 18 x + 71 = 0

Subtract 71 from both sides:

x^2 + 18 x = - 71

Add 81 to both sides:

x^2 + 18 x + 81 = 10

Write the left hand side as a square:

(x + 9) ^2 = 10

Take the square root of both sides:

x + 9 = sqrt (10) or x + 9 = - sqrt (10)

Subtract 9 from both sides:

x = sqrt (10) - 9 or x + 9 = - sqrt (10)

Subtract 9 from both sides:

Answer: x = sqrt (10) - 9 or x = - 9 - sqrt (10)