3x^2+8x-13=90

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Solution for 3x^2+8x-13=90 equation: 


Simplifying
3x2 + 8x + -13 = 90

Reorder the terms:
-13 + 8x + 3x2 = 90

Solving
-13 + 8x + 3x2 = 90

Solving for variable 'x'.

Reorder the terms:
-13 + -90 + 8x + 3x2 = 90 + -90

Combine like terms: -13 + -90 = -103
-103 + 8x + 3x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-103 + 8x + 3x2 = 0

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

Divide each side by '3'.
-34.33333333 + 2.666666667x + x2 = 0

Move the constant term to the right:

Add '34.33333333' to each side of the equation.
-34.33333333 + 2.666666667x + 34.33333333 + x2 = 0 + 34.33333333

Reorder the terms:
-34.33333333 + 34.33333333 + 2.666666667x + x2 = 0 + 34.33333333

Combine like terms: -34.33333333 + 34.33333333 = 0.00000000
0.00000000 + 2.666666667x + x2 = 0 + 34.33333333
2.666666667x + x2 = 0 + 34.33333333

Combine like terms: 0 + 34.33333333 = 34.33333333
2.666666667x + x2 = 34.33333333

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 = 34.33333333 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667x + x2 = 34.33333333 + 1.777777780

Combine like terms: 34.33333333 + 1.777777780 = 36.11111111
1.777777780 + 2.666666667x + x2 = 36.11111111

Factor a perfect square on the left side:
(x + 1.333333334)(x + 1.333333334) = 36.11111111

Calculate the square root of the right side: 6.009252126

Break this problem into two subproblems by setting 
(x + 1.333333334) equal to 6.009252126 and -6.009252126.


Subproblem 1
x + 1.333333334 = 6.009252126

Simplifying
x + 1.333333334 = 6.009252126

Reorder the terms:
1.333333334 + x = 6.009252126

Solving
1.333333334 + x = 6.009252126

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 = 6.009252126 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + x = 6.009252126 + -1.333333334
x = 6.009252126 + -1.333333334

Combine like terms: 6.009252126 + -1.333333334 = 4.675918792
x = 4.675918792

Simplifying
x = 4.675918792


Subproblem 2
x + 1.333333334 = -6.009252126

Simplifying
x + 1.333333334 = -6.009252126

Reorder the terms:
1.333333334 + x = -6.009252126

Solving
1.333333334 + x = -6.009252126

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 = -6.009252126 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + x = -6.009252126 + -1.333333334
x = -6.009252126 + -1.333333334

Combine like terms: -6.009252126 + -1.333333334 = -7.34258546
x = -7.34258546

Simplifying
x = -7.34258546


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.675918792, -7.34258546}

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