4x^2-147x-15=0

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Solution for 4x^2-147x-15=0 equation: 


Simplifying
4x2 + -147x + -15 = 0

Reorder the terms:
-15 + -147x + 4x2 = 0

Solving
-15 + -147x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-3.75 + -36.75x + x2 = 0

Move the constant term to the right:

Add '3.75' to each side of the equation.
-3.75 + -36.75x + 3.75 + x2 = 0 + 3.75

Reorder the terms:
-3.75 + 3.75 + -36.75x + x2 = 0 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + -36.75x + x2 = 0 + 3.75
-36.75x + x2 = 0 + 3.75

Combine like terms: 0 + 3.75 = 3.75
-36.75x + x2 = 3.75

The x term is -36.75x.  Take half its coefficient (-18.375).
Square it (337.640625) and add it to both sides.

Add '337.640625' to each side of the equation.
-36.75x + 337.640625 + x2 = 3.75 + 337.640625

Reorder the terms:
337.640625 + -36.75x + x2 = 3.75 + 337.640625

Combine like terms: 3.75 + 337.640625 = 341.390625
337.640625 + -36.75x + x2 = 341.390625

Factor a perfect square on the left side:
(x + -18.375)(x + -18.375) = 341.390625

Calculate the square root of the right side: 18.47675905

Break this problem into two subproblems by setting 
(x + -18.375) equal to 18.47675905 and -18.47675905.


Subproblem 1
x + -18.375 = 18.47675905

Simplifying
x + -18.375 = 18.47675905

Reorder the terms:
-18.375 + x = 18.47675905

Solving
-18.375 + x = 18.47675905

Solving for variable 'x'.

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

Add '18.375' to each side of the equation.
-18.375 + 18.375 + x = 18.47675905 + 18.375

Combine like terms: -18.375 + 18.375 = 0.000
0.000 + x = 18.47675905 + 18.375
x = 18.47675905 + 18.375

Combine like terms: 18.47675905 + 18.375 = 36.85175905
x = 36.85175905

Simplifying
x = 36.85175905


Subproblem 2
x + -18.375 = -18.47675905

Simplifying
x + -18.375 = -18.47675905

Reorder the terms:
-18.375 + x = -18.47675905

Solving
-18.375 + x = -18.47675905

Solving for variable 'x'.

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

Add '18.375' to each side of the equation.
-18.375 + 18.375 + x = -18.47675905 + 18.375

Combine like terms: -18.375 + 18.375 = 0.000
0.000 + x = -18.47675905 + 18.375
x = -18.47675905 + 18.375

Combine like terms: -18.47675905 + 18.375 = -0.10175905
x = -0.10175905

Simplifying
x = -0.10175905


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {36.85175905, -0.10175905}

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