4x^2-25x-50=0

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Solution for 4x^2-25x-50=0 equation: 


Simplifying
4x2 + -25x + -50 = 0

Reorder the terms:
-50 + -25x + 4x2 = 0

Solving
-50 + -25x + 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'.
-12.5 + -6.25x + x2 = 0

Move the constant term to the right:

Add '12.5' to each side of the equation.
-12.5 + -6.25x + 12.5 + x2 = 0 + 12.5

Reorder the terms:
-12.5 + 12.5 + -6.25x + x2 = 0 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + -6.25x + x2 = 0 + 12.5
-6.25x + x2 = 0 + 12.5

Combine like terms: 0 + 12.5 = 12.5
-6.25x + x2 = 12.5

The x term is -6.25x.  Take half its coefficient (-3.125).
Square it (9.765625) and add it to both sides.

Add '9.765625' to each side of the equation.
-6.25x + 9.765625 + x2 = 12.5 + 9.765625

Reorder the terms:
9.765625 + -6.25x + x2 = 12.5 + 9.765625

Combine like terms: 12.5 + 9.765625 = 22.265625
9.765625 + -6.25x + x2 = 22.265625

Factor a perfect square on the left side:
(x + -3.125)(x + -3.125) = 22.265625

Calculate the square root of the right side: 4.718646522

Break this problem into two subproblems by setting 
(x + -3.125) equal to 4.718646522 and -4.718646522.


Subproblem 1
x + -3.125 = 4.718646522

Simplifying
x + -3.125 = 4.718646522

Reorder the terms:
-3.125 + x = 4.718646522

Solving
-3.125 + x = 4.718646522

Solving for variable 'x'.

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

Add '3.125' to each side of the equation.
-3.125 + 3.125 + x = 4.718646522 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + x = 4.718646522 + 3.125
x = 4.718646522 + 3.125

Combine like terms: 4.718646522 + 3.125 = 7.843646522
x = 7.843646522

Simplifying
x = 7.843646522


Subproblem 2
x + -3.125 = -4.718646522

Simplifying
x + -3.125 = -4.718646522

Reorder the terms:
-3.125 + x = -4.718646522

Solving
-3.125 + x = -4.718646522

Solving for variable 'x'.

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

Add '3.125' to each side of the equation.
-3.125 + 3.125 + x = -4.718646522 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + x = -4.718646522 + 3.125
x = -4.718646522 + 3.125

Combine like terms: -4.718646522 + 3.125 = -1.593646522
x = -1.593646522

Simplifying
x = -1.593646522


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.843646522, -1.593646522}

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