4x^2+18x-15=0

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Solution for 4x^2+18x-15=0 equation: 


Simplifying
4x2 + 18x + -15 = 0

Reorder the terms:
-15 + 18x + 4x2 = 0

Solving
-15 + 18x + 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 + 4.5x + x2 = 0

Move the constant term to the right:

Add '3.75' to each side of the equation.
-3.75 + 4.5x + 3.75 + x2 = 0 + 3.75

Reorder the terms:
-3.75 + 3.75 + 4.5x + x2 = 0 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + 4.5x + x2 = 0 + 3.75
4.5x + x2 = 0 + 3.75

Combine like terms: 0 + 3.75 = 3.75
4.5x + x2 = 3.75

The x term is 4.5x.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5x + 5.0625 + x2 = 3.75 + 5.0625

Reorder the terms:
5.0625 + 4.5x + x2 = 3.75 + 5.0625

Combine like terms: 3.75 + 5.0625 = 8.8125
5.0625 + 4.5x + x2 = 8.8125

Factor a perfect square on the left side:
(x + 2.25)(x + 2.25) = 8.8125

Calculate the square root of the right side: 2.968585522

Break this problem into two subproblems by setting 
(x + 2.25) equal to 2.968585522 and -2.968585522.


Subproblem 1
x + 2.25 = 2.968585522

Simplifying
x + 2.25 = 2.968585522

Reorder the terms:
2.25 + x = 2.968585522

Solving
2.25 + x = 2.968585522

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = 2.968585522 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = 2.968585522 + -2.25
x = 2.968585522 + -2.25

Combine like terms: 2.968585522 + -2.25 = 0.718585522
x = 0.718585522

Simplifying
x = 0.718585522


Subproblem 2
x + 2.25 = -2.968585522

Simplifying
x + 2.25 = -2.968585522

Reorder the terms:
2.25 + x = -2.968585522

Solving
2.25 + x = -2.968585522

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = -2.968585522 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = -2.968585522 + -2.25
x = -2.968585522 + -2.25

Combine like terms: -2.968585522 + -2.25 = -5.218585522
x = -5.218585522

Simplifying
x = -5.218585522


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.718585522, -5.218585522}

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