FOLLOW THE PROCEDURE OUTLINED IN THIS SOLUTION:
Solve for x:
2 x^2+6 x-5 = 0
Divide both sides by 2:
x^2+3 x-5/2 = 0
Add 5/2 to both sides:
x^2+3 x = 5/2
Add 9/4 to both sides:
x^2+3 x+9/4 = 19/4
Write the left hand side as a square:
(x+3/2)^2 = 19/4
Take the square root of both sides:
x+3/2 = sqrt(19)/2 or x+3/2 = -sqrt(19)/2
Subtract 3/2 from both sides:
x = sqrt(19)/2-3/2 or x+3/2 = -sqrt(19)/2
Subtract 3/2 from both sides:
Answer: |x = sqrt(19)/2-3/2 or x = -3/2-sqrt(19)/2