4x^2+5x-15=0

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Solution for 4x^2+5x-15=0 equation: 


Simplifying
4x2 + 5x + -15 = 0

Reorder the terms:
-15 + 5x + 4x2 = 0

Solving
-15 + 5x + 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 + 1.25x + x2 = 0

Move the constant term to the right:

Add '3.75' to each side of the equation.
-3.75 + 1.25x + 3.75 + x2 = 0 + 3.75

Reorder the terms:
-3.75 + 3.75 + 1.25x + x2 = 0 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + 1.25x + x2 = 0 + 3.75
1.25x + x2 = 0 + 3.75

Combine like terms: 0 + 3.75 = 3.75
1.25x + x2 = 3.75

The x term is 1.25x.  Take half its coefficient (0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
1.25x + 0.390625 + x2 = 3.75 + 0.390625

Reorder the terms:
0.390625 + 1.25x + x2 = 3.75 + 0.390625

Combine like terms: 3.75 + 0.390625 = 4.140625
0.390625 + 1.25x + x2 = 4.140625

Factor a perfect square on the left side:
(x + 0.625)(x + 0.625) = 4.140625

Calculate the square root of the right side: 2.034852575

Break this problem into two subproblems by setting 
(x + 0.625) equal to 2.034852575 and -2.034852575.


Subproblem 1
x + 0.625 = 2.034852575

Simplifying
x + 0.625 = 2.034852575

Reorder the terms:
0.625 + x = 2.034852575

Solving
0.625 + x = 2.034852575

Solving for variable 'x'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + x = 2.034852575 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = 2.034852575 + -0.625
x = 2.034852575 + -0.625

Combine like terms: 2.034852575 + -0.625 = 1.409852575
x = 1.409852575

Simplifying
x = 1.409852575


Subproblem 2
x + 0.625 = -2.034852575

Simplifying
x + 0.625 = -2.034852575

Reorder the terms:
0.625 + x = -2.034852575

Solving
0.625 + x = -2.034852575

Solving for variable 'x'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + x = -2.034852575 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = -2.034852575 + -0.625
x = -2.034852575 + -0.625

Combine like terms: -2.034852575 + -0.625 = -2.659852575
x = -2.659852575

Simplifying
x = -2.659852575


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.409852575, -2.659852575}

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