4x^2-16x-15=0

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Solution for 4x^2-16x-15=0 equation: 


Simplifying
4x2 + -16x + -15 = 0

Reorder the terms:
-15 + -16x + 4x2 = 0

Solving
-15 + -16x + 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 + -4x + x2 = 0

Move the constant term to the right:

Add '3.75' to each side of the equation.
-3.75 + -4x + 3.75 + x2 = 0 + 3.75

Reorder the terms:
-3.75 + 3.75 + -4x + x2 = 0 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + -4x + x2 = 0 + 3.75
-4x + x2 = 0 + 3.75

Combine like terms: 0 + 3.75 = 3.75
-4x + x2 = 3.75

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 3.75 + 4

Reorder the terms:
4 + -4x + x2 = 3.75 + 4

Combine like terms: 3.75 + 4 = 7.75
4 + -4x + x2 = 7.75

Factor a perfect square on the left side:
(x + -2)(x + -2) = 7.75

Calculate the square root of the right side: 2.783882181

Break this problem into two subproblems by setting 
(x + -2) equal to 2.783882181 and -2.783882181.


Subproblem 1
x + -2 = 2.783882181

Simplifying
x + -2 = 2.783882181

Reorder the terms:
-2 + x = 2.783882181

Solving
-2 + x = 2.783882181

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 2.783882181 + 2

Combine like terms: -2 + 2 = 0
0 + x = 2.783882181 + 2
x = 2.783882181 + 2

Combine like terms: 2.783882181 + 2 = 4.783882181
x = 4.783882181

Simplifying
x = 4.783882181


Subproblem 2
x + -2 = -2.783882181

Simplifying
x + -2 = -2.783882181

Reorder the terms:
-2 + x = -2.783882181

Solving
-2 + x = -2.783882181

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -2.783882181 + 2

Combine like terms: -2 + 2 = 0
0 + x = -2.783882181 + 2
x = -2.783882181 + 2

Combine like terms: -2.783882181 + 2 = -0.783882181
x = -0.783882181

Simplifying
x = -0.783882181


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.783882181, -0.783882181}

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