x^2+x=1.52

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Solution for x^2+x=1.52 equation: 


Simplifying
x2 + x = 1.52

Reorder the terms:
x + x2 = 1.52

Solving
x + x2 = 1.52

Solving for variable 'x'.

Reorder the terms:
-1.52 + x + x2 = 1.52 + -1.52

Combine like terms: 1.52 + -1.52 = 0.00
-1.52 + x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '1.52' to each side of the equation.
-1.52 + x + 1.52 + x2 = 0.00 + 1.52

Reorder the terms:
-1.52 + 1.52 + x + x2 = 0.00 + 1.52

Combine like terms: -1.52 + 1.52 = 0.00
0.00 + x + x2 = 0.00 + 1.52
x + x2 = 0.00 + 1.52

Combine like terms: 0.00 + 1.52 = 1.52
x + x2 = 1.52

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.
x + 0.25 + x2 = 1.52 + 0.25

Reorder the terms:
0.25 + x + x2 = 1.52 + 0.25

Combine like terms: 1.52 + 0.25 = 1.77
0.25 + x + x2 = 1.77

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 1.77

Calculate the square root of the right side: 1.33041347

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.33041347 and -1.33041347.


Subproblem 1
x + 0.5 = 1.33041347

Simplifying
x + 0.5 = 1.33041347

Reorder the terms:
0.5 + x = 1.33041347

Solving
0.5 + x = 1.33041347

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 = 1.33041347 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.33041347 + -0.5
x = 1.33041347 + -0.5

Combine like terms: 1.33041347 + -0.5 = 0.83041347
x = 0.83041347

Simplifying
x = 0.83041347


Subproblem 2
x + 0.5 = -1.33041347

Simplifying
x + 0.5 = -1.33041347

Reorder the terms:
0.5 + x = -1.33041347

Solving
0.5 + x = -1.33041347

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 = -1.33041347 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.33041347 + -0.5
x = -1.33041347 + -0.5

Combine like terms: -1.33041347 + -0.5 = -1.83041347
x = -1.83041347

Simplifying
x = -1.83041347


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.83041347, -1.83041347}

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