Solve the equation by completing the square. Round to the nearest hundredth if necessary.
x^2+ 3x- 5 = 0
To solve the equation by completing the square, we need to rewrite it in the form (x + a)^2 = b, where a and b are constants.
First, move the constant term to the right side of the equation:
x^2 + 3x = 5
Next, we need to identify the coefficient of x and divide it by 2, then square the result:
(coefficient of x)/2 = (3/2)^2 = 9/4
Add this value to both sides of the equation:
x^2 + 3x + 9/4 = 5 + 9/4
Simplify the right side:
x^2 + 3x + 9/4 = 20/4 + 9/4
x^2 + 3x + 9/4 = 29/4
Now, rewrite the left side of the equation as a squared binomial:
(x + 3/2)^2 = 29/4
Taking the square root of both sides:
x + 3/2 = ±√(29/4)
Simplify the right side:
x + 3/2 = ±√29 / 2
Subtract 3/2 from both sides:
x = (-3/2) ± (√29 / 2)
Rounded to the nearest hundredth, the solutions are:
x ≈ -2.22 and x ≈ 0.22