13x^2+3510x-4290=0

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Solution for 13x^2+3510x-4290=0 equation: 


Simplifying
13x2 + 3510x + -4290 = 0

Reorder the terms:
-4290 + 3510x + 13x2 = 0

Solving
-4290 + 3510x + 13x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '13'.
13(-330 + 270x + x2) = 0

Ignore the factor 13.

Subproblem 1
Set the factor '(-330 + 270x + x2)' equal to zero and attempt to solve:

Simplifying
-330 + 270x + x2 = 0

Solving
-330 + 270x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '330' to each side of the equation.
-330 + 270x + 330 + x2 = 0 + 330

Reorder the terms:
-330 + 330 + 270x + x2 = 0 + 330

Combine like terms: -330 + 330 = 0
0 + 270x + x2 = 0 + 330
270x + x2 = 0 + 330

Combine like terms: 0 + 330 = 330
270x + x2 = 330

The x term is 270x.  Take half its coefficient (135).
Square it (18225) and add it to both sides.

Add '18225' to each side of the equation.
270x + 18225 + x2 = 330 + 18225

Reorder the terms:
18225 + 270x + x2 = 330 + 18225

Combine like terms: 330 + 18225 = 18555
18225 + 270x + x2 = 18555

Factor a perfect square on the left side:
(x + 135)(x + 135) = 18555

Calculate the square root of the right side: 136.216739059

Break this problem into two subproblems by setting 
(x + 135) equal to 136.216739059 and -136.216739059.


Subproblem 1
x + 135 = 136.216739059

Simplifying
x + 135 = 136.216739059

Reorder the terms:
135 + x = 136.216739059

Solving
135 + x = 136.216739059

Solving for variable 'x'.

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

Add '-135' to each side of the equation.
135 + -135 + x = 136.216739059 + -135

Combine like terms: 135 + -135 = 0
0 + x = 136.216739059 + -135
x = 136.216739059 + -135

Combine like terms: 136.216739059 + -135 = 1.216739059
x = 1.216739059

Simplifying
x = 1.216739059


Subproblem 2
x + 135 = -136.216739059

Simplifying
x + 135 = -136.216739059

Reorder the terms:
135 + x = -136.216739059

Solving
135 + x = -136.216739059

Solving for variable 'x'.

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

Add '-135' to each side of the equation.
135 + -135 + x = -136.216739059 + -135

Combine like terms: 135 + -135 = 0
0 + x = -136.216739059 + -135
x = -136.216739059 + -135

Combine like terms: -136.216739059 + -135 = -271.216739059
x = -271.216739059

Simplifying
x = -271.216739059


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.216739059, -271.216739059}
Solution
x = {1.216739059, -271.216739059}

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