4x^2+12.5x-15=0

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Solution for 4x^2+12.5x-15=0 equation: 


Simplifying
4x2 + 12.5x + -15 = 0

Reorder the terms:
-15 + 12.5x + 4x2 = 0

Solving
-15 + 12.5x + 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 + 3.125x + x2 = 0

Move the constant term to the right:

Add '3.75' to each side of the equation.
-3.75 + 3.125x + 3.75 + x2 = 0 + 3.75

Reorder the terms:
-3.75 + 3.75 + 3.125x + x2 = 0 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + 3.125x + x2 = 0 + 3.75
3.125x + x2 = 0 + 3.75

Combine like terms: 0 + 3.75 = 3.75
3.125x + x2 = 3.75

The x term is 3.125x.  Take half its coefficient (1.5625).
Square it (2.44140625) and add it to both sides.

Add '2.44140625' to each side of the equation.
3.125x + 2.44140625 + x2 = 3.75 + 2.44140625

Reorder the terms:
2.44140625 + 3.125x + x2 = 3.75 + 2.44140625

Combine like terms: 3.75 + 2.44140625 = 6.19140625
2.44140625 + 3.125x + x2 = 6.19140625

Factor a perfect square on the left side:
(x + 1.5625)(x + 1.5625) = 6.19140625

Calculate the square root of the right side: 2.488253655

Break this problem into two subproblems by setting 
(x + 1.5625) equal to 2.488253655 and -2.488253655.


Subproblem 1
x + 1.5625 = 2.488253655

Simplifying
x + 1.5625 = 2.488253655

Reorder the terms:
1.5625 + x = 2.488253655

Solving
1.5625 + x = 2.488253655

Solving for variable 'x'.

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

Add '-1.5625' to each side of the equation.
1.5625 + -1.5625 + x = 2.488253655 + -1.5625

Combine like terms: 1.5625 + -1.5625 = 0.0000
0.0000 + x = 2.488253655 + -1.5625
x = 2.488253655 + -1.5625

Combine like terms: 2.488253655 + -1.5625 = 0.925753655
x = 0.925753655

Simplifying
x = 0.925753655


Subproblem 2
x + 1.5625 = -2.488253655

Simplifying
x + 1.5625 = -2.488253655

Reorder the terms:
1.5625 + x = -2.488253655

Solving
1.5625 + x = -2.488253655

Solving for variable 'x'.

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

Add '-1.5625' to each side of the equation.
1.5625 + -1.5625 + x = -2.488253655 + -1.5625

Combine like terms: 1.5625 + -1.5625 = 0.0000
0.0000 + x = -2.488253655 + -1.5625
x = -2.488253655 + -1.5625

Combine like terms: -2.488253655 + -1.5625 = -4.050753655
x = -4.050753655

Simplifying
x = -4.050753655


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.925753655, -4.050753655}

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