4x^2+70x-460=0

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Solution for 4x^2+70x-460=0 equation: 


Simplifying
4x2 + 70x + -460 = 0

Reorder the terms:
-460 + 70x + 4x2 = 0

Solving
-460 + 70x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-230 + 35x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-230 + 35x + 2x2)' equal to zero and attempt to solve:

Simplifying
-230 + 35x + 2x2 = 0

Solving
-230 + 35x + 2x2 = 0

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

Divide each side by '2'.
-115 + 17.5x + x2 = 0

Move the constant term to the right:

Add '115' to each side of the equation.
-115 + 17.5x + 115 + x2 = 0 + 115

Reorder the terms:
-115 + 115 + 17.5x + x2 = 0 + 115

Combine like terms: -115 + 115 = 0
0 + 17.5x + x2 = 0 + 115
17.5x + x2 = 0 + 115

Combine like terms: 0 + 115 = 115
17.5x + x2 = 115

The x term is 17.5x.  Take half its coefficient (8.75).
Square it (76.5625) and add it to both sides.

Add '76.5625' to each side of the equation.
17.5x + 76.5625 + x2 = 115 + 76.5625

Reorder the terms:
76.5625 + 17.5x + x2 = 115 + 76.5625

Combine like terms: 115 + 76.5625 = 191.5625
76.5625 + 17.5x + x2 = 191.5625

Factor a perfect square on the left side:
(x + 8.75)(x + 8.75) = 191.5625

Calculate the square root of the right side: 13.840610536

Break this problem into two subproblems by setting 
(x + 8.75) equal to 13.840610536 and -13.840610536.


Subproblem 1
x + 8.75 = 13.840610536

Simplifying
x + 8.75 = 13.840610536

Reorder the terms:
8.75 + x = 13.840610536

Solving
8.75 + x = 13.840610536

Solving for variable 'x'.

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

Add '-8.75' to each side of the equation.
8.75 + -8.75 + x = 13.840610536 + -8.75

Combine like terms: 8.75 + -8.75 = 0.00
0.00 + x = 13.840610536 + -8.75
x = 13.840610536 + -8.75

Combine like terms: 13.840610536 + -8.75 = 5.090610536
x = 5.090610536

Simplifying
x = 5.090610536


Subproblem 2
x + 8.75 = -13.840610536

Simplifying
x + 8.75 = -13.840610536

Reorder the terms:
8.75 + x = -13.840610536

Solving
8.75 + x = -13.840610536

Solving for variable 'x'.

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

Add '-8.75' to each side of the equation.
8.75 + -8.75 + x = -13.840610536 + -8.75

Combine like terms: 8.75 + -8.75 = 0.00
0.00 + x = -13.840610536 + -8.75
x = -13.840610536 + -8.75

Combine like terms: -13.840610536 + -8.75 = -22.590610536
x = -22.590610536

Simplifying
x = -22.590610536


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.090610536, -22.590610536}
Solution
x = {5.090610536, -22.590610536}

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