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

Question

x^2+8x=10

1.1, 9.1
1.1, -9.1
-1.1, 9.1
-1.1, -9.1

Answer 1

To solve the equation by completing the square, we need to rearrange the equation to make it look like a perfect square trinomial.

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

Now, take the square root of both sides to solve for x:

x + 4 = ±√26
x = -4 ±√26

Rounded to the nearest tenth, we get:
x ≈ -4 + √26 ≈ 1.1
or
x ≈ -4 - √26 ≈ -9.1

Therefore, the solutions are:
1.1, -9.1.