2x^2+2x-1.5=0

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Solution for 2x^2+2x-1.5=0 equation:


Simplifying
2x2 + 2x + -1.5 = 0

Reorder the terms:
-1.5 + 2x + 2x2 = 0

Solving
-1.5 + 2x + 2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-0.75 + x + x2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + x + 0.75 + x2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + x + x2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x + x2 = 0 + 0.75
x + x2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
x + x2 = 0.75

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 0.75 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 0.75 + 0.25

Combine like terms: 0.75 + 0.25 = 1
1.25 + x2 = 1

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 1

Calculate the square root of the right side: 1

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1 and -1.

Subproblem 1

x + 0.5 = 1 Simplifying x + 0.5 = 1 Reorder the terms: 0.5 + x = 1 Solving 0.5 + x = 1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1 + -0.5 x = 1 + -0.5 Combine like terms: 1 + -0.5 = 0.5 x = 0.5 Simplifying x = 0.5

Subproblem 2

x + 0.5 = -1 Simplifying x + 0.5 = -1 Reorder the terms: 0.5 + x = -1 Solving 0.5 + x = -1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1 + -0.5 x = -1 + -0.5 Combine like terms: -1 + -0.5 = -1.5 x = -1.5 Simplifying x = -1.5

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.5, -1.5}

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