4x^2+70x+300=114

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Solution for 4x^2+70x+300=114 equation: 


Simplifying
4x2 + 70x + 300 = 114

Reorder the terms:
300 + 70x + 4x2 = 114

Solving
300 + 70x + 4x2 = 114

Solving for variable 'x'.

Reorder the terms:
300 + -114 + 70x + 4x2 = 114 + -114

Combine like terms: 300 + -114 = 186
186 + 70x + 4x2 = 114 + -114

Combine like terms: 114 + -114 = 0
186 + 70x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(93 + 35x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(93 + 35x + 2x2)' equal to zero and attempt to solve:

Simplifying
93 + 35x + 2x2 = 0

Solving
93 + 35x + 2x2 = 0

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

Divide each side by '2'.
46.5 + 17.5x + x2 = 0

Move the constant term to the right:

Add '-46.5' to each side of the equation.
46.5 + 17.5x + -46.5 + x2 = 0 + -46.5

Reorder the terms:
46.5 + -46.5 + 17.5x + x2 = 0 + -46.5

Combine like terms: 46.5 + -46.5 = 0.0
0.0 + 17.5x + x2 = 0 + -46.5
17.5x + x2 = 0 + -46.5

Combine like terms: 0 + -46.5 = -46.5
17.5x + x2 = -46.5

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 = -46.5 + 76.5625

Reorder the terms:
76.5625 + 17.5x + x2 = -46.5 + 76.5625

Combine like terms: -46.5 + 76.5625 = 30.0625
76.5625 + 17.5x + x2 = 30.0625

Factor a perfect square on the left side:
(x + 8.75)(x + 8.75) = 30.0625

Calculate the square root of the right side: 5.48292805

Break this problem into two subproblems by setting 
(x + 8.75) equal to 5.48292805 and -5.48292805.


Subproblem 1
x + 8.75 = 5.48292805

Simplifying
x + 8.75 = 5.48292805

Reorder the terms:
8.75 + x = 5.48292805

Solving
8.75 + x = 5.48292805

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 = 5.48292805 + -8.75

Combine like terms: 8.75 + -8.75 = 0.00
0.00 + x = 5.48292805 + -8.75
x = 5.48292805 + -8.75

Combine like terms: 5.48292805 + -8.75 = -3.26707195
x = -3.26707195

Simplifying
x = -3.26707195


Subproblem 2
x + 8.75 = -5.48292805

Simplifying
x + 8.75 = -5.48292805

Reorder the terms:
8.75 + x = -5.48292805

Solving
8.75 + x = -5.48292805

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 = -5.48292805 + -8.75

Combine like terms: 8.75 + -8.75 = 0.00
0.00 + x = -5.48292805 + -8.75
x = -5.48292805 + -8.75

Combine like terms: -5.48292805 + -8.75 = -14.23292805
x = -14.23292805

Simplifying
x = -14.23292805


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.26707195, -14.23292805}
Solution
x = {-3.26707195, -14.23292805}

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