Solve the equation by completing the square. Round to the nearest hundredth if necessary.
x^2 + 3x - 5 = 0
To solve the equation x^2 + 3x - 5 = 0 by completing the square, we need to rearrange the equation by moving the constant term to the right side:
x^2 + 3x = 5
Now we will complete the square by adding the square of half the coefficient of x to both sides of the equation. In this case, the coefficient of x is 3, so half of it is 3/2, and the square of 3/2 is 9/4:
x^2 + 3x + 9/4 = 5 + 9/4
Simplifying the right side:
x^2 + 3x + 9/4 = 20/4 + 9/4
x^2 + 3x + 9/4 = 29/4
Next, we can write the left side of the equation as a perfect square trinomial:
(x + 3/2)^2 = 29/4
To solve for x, we take the square root of both sides:
√((x + 3/2)^2) = ±√(29/4)
(x + 3/2) = ±√29/2
Now we can solve for x by subtracting 3/2 from both sides:
x = -3/2 ± √29/2
Rounded to the nearest hundredth, x ≈ -2.37 or x ≈ 0.37.