(x)(x)-15x-4=0

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Solution for (x)(x)-15x-4=0 equation:


Simplifying
(x)(x) + -15x + -4 = 0

Multiply x * x
x2 + -15x + -4 = 0

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

Solving
-4 + -15x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -15x + 4 + x2 = 0 + 4

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

Combine like terms: -4 + 4 = 0
0 + -15x + x2 = 0 + 4
-15x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-15x + x2 = 4

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 = 4 + 56.25

Reorder the terms:
56.25 + -15x + x2 = 4 + 56.25

Combine like terms: 4 + 56.25 = 60.25
56.25 + -15x + x2 = 60.25

Factor a perfect square on the left side:
(x + -7.5)(x + -7.5) = 60.25

Calculate the square root of the right side: 7.762087348

Break this problem into two subproblems by setting 
(x + -7.5) equal to 7.762087348 and -7.762087348.

Subproblem 1

x + -7.5 = 7.762087348 Simplifying x + -7.5 = 7.762087348 Reorder the terms: -7.5 + x = 7.762087348 Solving -7.5 + x = 7.762087348 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 = 7.762087348 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 7.762087348 + 7.5 x = 7.762087348 + 7.5 Combine like terms: 7.762087348 + 7.5 = 15.262087348 x = 15.262087348 Simplifying x = 15.262087348

Subproblem 2

x + -7.5 = -7.762087348 Simplifying x + -7.5 = -7.762087348 Reorder the terms: -7.5 + x = -7.762087348 Solving -7.5 + x = -7.762087348 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 = -7.762087348 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -7.762087348 + 7.5 x = -7.762087348 + 7.5 Combine like terms: -7.762087348 + 7.5 = -0.262087348 x = -0.262087348 Simplifying x = -0.262087348

Solution

The solution to the problem is based on the solutions from the subproblems. x = {15.262087348, -0.262087348}

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