4x^2+60x+46=0

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Solution for 4x^2+60x+46=0 equation: 


Simplifying
4x2 + 60x + 46 = 0

Reorder the terms:
46 + 60x + 4x2 = 0

Solving
46 + 60x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(23 + 30x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(23 + 30x + 2x2)' equal to zero and attempt to solve:

Simplifying
23 + 30x + 2x2 = 0

Solving
23 + 30x + 2x2 = 0

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

Divide each side by '2'.
11.5 + 15x + x2 = 0

Move the constant term to the right:

Add '-11.5' to each side of the equation.
11.5 + 15x + -11.5 + x2 = 0 + -11.5

Reorder the terms:
11.5 + -11.5 + 15x + x2 = 0 + -11.5

Combine like terms: 11.5 + -11.5 = 0.0
0.0 + 15x + x2 = 0 + -11.5
15x + x2 = 0 + -11.5

Combine like terms: 0 + -11.5 = -11.5
15x + x2 = -11.5

The x term is 15x.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15x + 56.25 + x2 = -11.5 + 56.25

Reorder the terms:
56.25 + 15x + x2 = -11.5 + 56.25

Combine like terms: -11.5 + 56.25 = 44.75
56.25 + 15x + x2 = 44.75

Factor a perfect square on the left side:
(x + 7.5)(x + 7.5) = 44.75

Calculate the square root of the right side: 6.68954408

Break this problem into two subproblems by setting 
(x + 7.5) equal to 6.68954408 and -6.68954408.


Subproblem 1
x + 7.5 = 6.68954408

Simplifying
x + 7.5 = 6.68954408

Reorder the terms:
7.5 + x = 6.68954408

Solving
7.5 + x = 6.68954408

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = 6.68954408 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = 6.68954408 + -7.5
x = 6.68954408 + -7.5

Combine like terms: 6.68954408 + -7.5 = -0.81045592
x = -0.81045592

Simplifying
x = -0.81045592


Subproblem 2
x + 7.5 = -6.68954408

Simplifying
x + 7.5 = -6.68954408

Reorder the terms:
7.5 + x = -6.68954408

Solving
7.5 + x = -6.68954408

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = -6.68954408 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = -6.68954408 + -7.5
x = -6.68954408 + -7.5

Combine like terms: -6.68954408 + -7.5 = -14.18954408
x = -14.18954408

Simplifying
x = -14.18954408


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.81045592, -14.18954408}
Solution
x = {-0.81045592, -14.18954408}

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