4x^2+5x-25=0

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Solution for 4x^2+5x-25=0 equation: 


Simplifying
4x2 + 5x + -25 = 0

Reorder the terms:
-25 + 5x + 4x2 = 0

Solving
-25 + 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'.
-6.25 + 1.25x + x2 = 0

Move the constant term to the right:

Add '6.25' to each side of the equation.
-6.25 + 1.25x + 6.25 + x2 = 0 + 6.25

Reorder the terms:
-6.25 + 6.25 + 1.25x + x2 = 0 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + 1.25x + x2 = 0 + 6.25
1.25x + x2 = 0 + 6.25

Combine like terms: 0 + 6.25 = 6.25
1.25x + x2 = 6.25

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 = 6.25 + 0.390625

Reorder the terms:
0.390625 + 1.25x + x2 = 6.25 + 0.390625

Combine like terms: 6.25 + 0.390625 = 6.640625
0.390625 + 1.25x + x2 = 6.640625

Factor a perfect square on the left side:
(x + 0.625)(x + 0.625) = 6.640625

Calculate the square root of the right side: 2.576941016

Break this problem into two subproblems by setting 
(x + 0.625) equal to 2.576941016 and -2.576941016.


Subproblem 1
x + 0.625 = 2.576941016

Simplifying
x + 0.625 = 2.576941016

Reorder the terms:
0.625 + x = 2.576941016

Solving
0.625 + x = 2.576941016

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 = 2.576941016 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = 2.576941016 + -0.625
x = 2.576941016 + -0.625

Combine like terms: 2.576941016 + -0.625 = 1.951941016
x = 1.951941016

Simplifying
x = 1.951941016


Subproblem 2
x + 0.625 = -2.576941016

Simplifying
x + 0.625 = -2.576941016

Reorder the terms:
0.625 + x = -2.576941016

Solving
0.625 + x = -2.576941016

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 = -2.576941016 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = -2.576941016 + -0.625
x = -2.576941016 + -0.625

Combine like terms: -2.576941016 + -0.625 = -3.201941016
x = -3.201941016

Simplifying
x = -3.201941016


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.951941016, -3.201941016}

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