(x*x)+x=7.4

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Solution for (x*x)+x=7.4 equation: 


Simplifying
(x * x) + x = 7.4

Multiply x * x
(x2) + x = 7.4
x2 + x = 7.4

Reorder the terms:
x + x2 = 7.4

Solving
x + x2 = 7.4

Solving for variable 'x'.

Reorder the terms:
-7.4 + x + x2 = 7.4 + -7.4

Combine like terms: 7.4 + -7.4 = 0.0
-7.4 + x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '7.4' to each side of the equation.
-7.4 + x + 7.4 + x2 = 0.0 + 7.4

Reorder the terms:
-7.4 + 7.4 + x + x2 = 0.0 + 7.4

Combine like terms: -7.4 + 7.4 = 0.0
0.0 + x + x2 = 0.0 + 7.4
x + x2 = 0.0 + 7.4

Combine like terms: 0.0 + 7.4 = 7.4
x + x2 = 7.4

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 = 7.4 + 0.25

Reorder the terms:
0.25 + x + x2 = 7.4 + 0.25

Combine like terms: 7.4 + 0.25 = 7.65
0.25 + x + x2 = 7.65

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 7.65

Calculate the square root of the right side: 2.765863337

Break this problem into two subproblems by setting 
(x + 0.5) equal to 2.765863337 and -2.765863337.


Subproblem 1
x + 0.5 = 2.765863337

Simplifying
x + 0.5 = 2.765863337

Reorder the terms:
0.5 + x = 2.765863337

Solving
0.5 + x = 2.765863337

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 = 2.765863337 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 2.765863337 + -0.5
x = 2.765863337 + -0.5

Combine like terms: 2.765863337 + -0.5 = 2.265863337
x = 2.265863337

Simplifying
x = 2.265863337


Subproblem 2
x + 0.5 = -2.765863337

Simplifying
x + 0.5 = -2.765863337

Reorder the terms:
0.5 + x = -2.765863337

Solving
0.5 + x = -2.765863337

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 = -2.765863337 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -2.765863337 + -0.5
x = -2.765863337 + -0.5

Combine like terms: -2.765863337 + -0.5 = -3.265863337
x = -3.265863337

Simplifying
x = -3.265863337


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.265863337, -3.265863337}

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