100x+15x^2-368=

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Solution for 100x+15x^2-368= equation: 


Simplifying
100x + 15x2 + -368 = 0

Reorder the terms:
-368 + 100x + 15x2 = 0

Solving
-368 + 100x + 15x2 = 0

Solving for variable 'x'.

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

Divide each side by '15'.
-24.53333333 + 6.666666667x + x2 = 0

Move the constant term to the right:

Add '24.53333333' to each side of the equation.
-24.53333333 + 6.666666667x + 24.53333333 + x2 = 0 + 24.53333333

Reorder the terms:
-24.53333333 + 24.53333333 + 6.666666667x + x2 = 0 + 24.53333333

Combine like terms: -24.53333333 + 24.53333333 = 0.00000000
0.00000000 + 6.666666667x + x2 = 0 + 24.53333333
6.666666667x + x2 = 0 + 24.53333333

Combine like terms: 0 + 24.53333333 = 24.53333333
6.666666667x + x2 = 24.53333333

The x term is 6.666666667x.  Take half its coefficient (3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
6.666666667x + 11.11111112 + x2 = 24.53333333 + 11.11111112

Reorder the terms:
11.11111112 + 6.666666667x + x2 = 24.53333333 + 11.11111112

Combine like terms: 24.53333333 + 11.11111112 = 35.64444445
11.11111112 + 6.666666667x + x2 = 35.64444445

Factor a perfect square on the left side:
(x + 3.333333334)(x + 3.333333334) = 35.64444445

Calculate the square root of the right side: 5.970296848

Break this problem into two subproblems by setting 
(x + 3.333333334) equal to 5.970296848 and -5.970296848.


Subproblem 1
x + 3.333333334 = 5.970296848

Simplifying
x + 3.333333334 = 5.970296848

Reorder the terms:
3.333333334 + x = 5.970296848

Solving
3.333333334 + x = 5.970296848

Solving for variable 'x'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + x = 5.970296848 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + x = 5.970296848 + -3.333333334
x = 5.970296848 + -3.333333334

Combine like terms: 5.970296848 + -3.333333334 = 2.636963514
x = 2.636963514

Simplifying
x = 2.636963514


Subproblem 2
x + 3.333333334 = -5.970296848

Simplifying
x + 3.333333334 = -5.970296848

Reorder the terms:
3.333333334 + x = -5.970296848

Solving
3.333333334 + x = -5.970296848

Solving for variable 'x'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + x = -5.970296848 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + x = -5.970296848 + -3.333333334
x = -5.970296848 + -3.333333334

Combine like terms: -5.970296848 + -3.333333334 = -9.303630182
x = -9.303630182

Simplifying
x = -9.303630182


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.636963514, -9.303630182}

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