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:

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

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step-by-step explanation: