Solve the equation by completing the square. Round to the nearest tenth.

Question

x squared plus 8 x equals 10

Answer 1

To solve by completing the square, first move the constant term (10) to the right side of the equation:

x^2 + 8x = 10
x^2 + 8x - 10 = 0

Now complete the square by taking half of the coefficient of x, squaring it, and adding it to both sides of the equation:

x^2 + 8x + 16 = 10 + 16
(x + 4)^2 = 26

Now, take the square root of both sides:

x + 4 = ±√26
x = -4 ±√26

To round to the nearest tenth:
x ≈ -4 + 5.1 ≈ 1.1
x ≈ -4 - 5.1 ≈ -9.1

Therefore the solutions are x ≈ 1.1 and x ≈ -9.1.