-0.5x^2+x+2.88=0

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Solution for -0.5x^2+x+2.88=0 equation: 


Simplifying
-0.5x2 + x + 2.88 = 0

Reorder the terms:
2.88 + x + -0.5x2 = 0

Solving
2.88 + x + -0.5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.5 the coefficient of the squared term: 

Divide each side by '-0.5'.
-5.76 + -2x + x2 = 0

Move the constant term to the right:

Add '5.76' to each side of the equation.
-5.76 + -2x + 5.76 + x2 = 0 + 5.76

Reorder the terms:
-5.76 + 5.76 + -2x + x2 = 0 + 5.76

Combine like terms: -5.76 + 5.76 = 0.00
0.00 + -2x + x2 = 0 + 5.76
-2x + x2 = 0 + 5.76

Combine like terms: 0 + 5.76 = 5.76
-2x + x2 = 5.76

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.
-2x + 0.25 + x2 = 5.76 + 0.25

Reorder the terms:
0.25 + -2x + x2 = 5.76 + 0.25

Combine like terms: 5.76 + 0.25 = 6.01
0.25 + -2x + x2 = 6.01

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 6.01

Calculate the square root of the right side: 2.451530134

Break this problem into two subproblems by setting 
(x + 0.5) equal to 2.451530134 and -2.451530134.


Subproblem 1
x + 0.5 = 2.451530134

Simplifying
x + 0.5 = 2.451530134

Reorder the terms:
0.5 + x = 2.451530134

Solving
0.5 + x = 2.451530134

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 = 2.451530134 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 2.451530134 + -0.5
x = 2.451530134 + -0.5

Combine like terms: 2.451530134 + -0.5 = 1.951530134
x = 1.951530134

Simplifying
x = 1.951530134


Subproblem 2
x + 0.5 = -2.451530134

Simplifying
x + 0.5 = -2.451530134

Reorder the terms:
0.5 + x = -2.451530134

Solving
0.5 + x = -2.451530134

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 = -2.451530134 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -2.451530134 + -0.5
x = -2.451530134 + -0.5

Combine like terms: -2.451530134 + -0.5 = -2.951530134
x = -2.951530134

Simplifying
x = -2.951530134


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.951530134, -2.951530134}

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