9.2=40x+15x^2

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Solution for 9.2=40x+15x^2 equation: 


Simplifying
9.2 = 40x + 15x2

Solving
9.2 = 40x + 15x2

Solving for variable 'x'.

Reorder the terms:
9.2 + -40x + -15x2 = 40x + -40x + 15x2 + -15x2

Combine like terms: 40x + -40x = 0
9.2 + -40x + -15x2 = 0 + 15x2 + -15x2
9.2 + -40x + -15x2 = 15x2 + -15x2

Combine like terms: 15x2 + -15x2 = 0
9.2 + -40x + -15x2 = 0

Begin completing the square.  Divide all terms by
-15 the coefficient of the squared term: 

Divide each side by '-15'.
-0.6133333333 + 2.666666667x + x2 = 0

Move the constant term to the right:

Add '0.6133333333' to each side of the equation.
-0.6133333333 + 2.666666667x + 0.6133333333 + x2 = 0 + 0.6133333333

Reorder the terms:
-0.6133333333 + 0.6133333333 + 2.666666667x + x2 = 0 + 0.6133333333

Combine like terms: -0.6133333333 + 0.6133333333 = 0.0000000000
0.0000000000 + 2.666666667x + x2 = 0 + 0.6133333333
2.666666667x + x2 = 0 + 0.6133333333

Combine like terms: 0 + 0.6133333333 = 0.6133333333
2.666666667x + x2 = 0.6133333333

The x term is 2.666666667x.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667x + 1.777777780 + x2 = 0.6133333333 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667x + x2 = 0.6133333333 + 1.777777780

Combine like terms: 0.6133333333 + 1.777777780 = 2.3911111133
1.777777780 + 2.666666667x + x2 = 2.3911111133

Factor a perfect square on the left side:
(x + 1.333333334)(x + 1.333333334) = 2.3911111133

Calculate the square root of the right side: 1.546321801

Break this problem into two subproblems by setting 
(x + 1.333333334) equal to 1.546321801 and -1.546321801.


Subproblem 1
x + 1.333333334 = 1.546321801

Simplifying
x + 1.333333334 = 1.546321801

Reorder the terms:
1.333333334 + x = 1.546321801

Solving
1.333333334 + x = 1.546321801

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + x = 1.546321801 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + x = 1.546321801 + -1.333333334
x = 1.546321801 + -1.333333334

Combine like terms: 1.546321801 + -1.333333334 = 0.212988467
x = 0.212988467

Simplifying
x = 0.212988467


Subproblem 2
x + 1.333333334 = -1.546321801

Simplifying
x + 1.333333334 = -1.546321801

Reorder the terms:
1.333333334 + x = -1.546321801

Solving
1.333333334 + x = -1.546321801

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + x = -1.546321801 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + x = -1.546321801 + -1.333333334
x = -1.546321801 + -1.333333334

Combine like terms: -1.546321801 + -1.333333334 = -2.879655135
x = -2.879655135

Simplifying
x = -2.879655135


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.212988467, -2.879655135}

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