4(x^2+19x-315)=0

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Solution for 4(x^2+19x-315)=0 equation: 


Simplifying
4(x2 + 19x + -315) = 0

Reorder the terms:
4(-315 + 19x + x2) = 0
(-315 * 4 + 19x * 4 + x2 * 4) = 0
(-1260 + 76x + 4x2) = 0

Solving
-1260 + 76x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-315 + 19x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-315 + 19x + x2)' equal to zero and attempt to solve:

Simplifying
-315 + 19x + x2 = 0

Solving
-315 + 19x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '315' to each side of the equation.
-315 + 19x + 315 + x2 = 0 + 315

Reorder the terms:
-315 + 315 + 19x + x2 = 0 + 315

Combine like terms: -315 + 315 = 0
0 + 19x + x2 = 0 + 315
19x + x2 = 0 + 315

Combine like terms: 0 + 315 = 315
19x + x2 = 315

The x term is 19x.  Take half its coefficient (9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
19x + 90.25 + x2 = 315 + 90.25

Reorder the terms:
90.25 + 19x + x2 = 315 + 90.25

Combine like terms: 315 + 90.25 = 405.25
90.25 + 19x + x2 = 405.25

Factor a perfect square on the left side:
(x + 9.5)(x + 9.5) = 405.25

Calculate the square root of the right side: 20.130822139

Break this problem into two subproblems by setting 
(x + 9.5) equal to 20.130822139 and -20.130822139.


Subproblem 1
x + 9.5 = 20.130822139

Simplifying
x + 9.5 = 20.130822139

Reorder the terms:
9.5 + x = 20.130822139

Solving
9.5 + x = 20.130822139

Solving for variable 'x'.

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

Add '-9.5' to each side of the equation.
9.5 + -9.5 + x = 20.130822139 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + x = 20.130822139 + -9.5
x = 20.130822139 + -9.5

Combine like terms: 20.130822139 + -9.5 = 10.630822139
x = 10.630822139

Simplifying
x = 10.630822139


Subproblem 2
x + 9.5 = -20.130822139

Simplifying
x + 9.5 = -20.130822139

Reorder the terms:
9.5 + x = -20.130822139

Solving
9.5 + x = -20.130822139

Solving for variable 'x'.

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

Add '-9.5' to each side of the equation.
9.5 + -9.5 + x = -20.130822139 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + x = -20.130822139 + -9.5
x = -20.130822139 + -9.5

Combine like terms: -20.130822139 + -9.5 = -29.630822139
x = -29.630822139

Simplifying
x = -29.630822139


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.630822139, -29.630822139}
Solution
x = {10.630822139, -29.630822139}

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