0=4x^2-5x-50

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Solution for 0=4x^2-5x-50 equation:


Simplifying
0 = 4x2 + -5x + -50

Reorder the terms:
0 = -50 + -5x + 4x2

Solving
0 = -50 + -5x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + 50 = 50
50 + 5x + -4x2 = -50 + -5x + 4x2 + 50 + 5x + -4x2

Reorder the terms:
50 + 5x + -4x2 = -50 + 50 + -5x + 5x + 4x2 + -4x2

Combine like terms: -50 + 50 = 0
50 + 5x + -4x2 = 0 + -5x + 5x + 4x2 + -4x2
50 + 5x + -4x2 = -5x + 5x + 4x2 + -4x2

Combine like terms: -5x + 5x = 0
50 + 5x + -4x2 = 0 + 4x2 + -4x2
50 + 5x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
50 + 5x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-12.5 + -1.25x + x2 = 0

Move the constant term to the right:

Add '12.5' to each side of the equation.
-12.5 + -1.25x + 12.5 + x2 = 0 + 12.5

Reorder the terms:
-12.5 + 12.5 + -1.25x + x2 = 0 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + -1.25x + x2 = 0 + 12.5
-1.25x + x2 = 0 + 12.5

Combine like terms: 0 + 12.5 = 12.5
-1.25x + x2 = 12.5

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 = 12.5 + 0.390625

Reorder the terms:
0.390625 + -1.25x + x2 = 12.5 + 0.390625

Combine like terms: 12.5 + 0.390625 = 12.890625
0.390625 + -1.25x + x2 = 12.890625

Factor a perfect square on the left side:
(x + -0.625)(x + -0.625) = 12.890625

Calculate the square root of the right side: 3.590351654

Break this problem into two subproblems by setting 
(x + -0.625) equal to 3.590351654 and -3.590351654.

Subproblem 1

x + -0.625 = 3.590351654 Simplifying x + -0.625 = 3.590351654 Reorder the terms: -0.625 + x = 3.590351654 Solving -0.625 + x = 3.590351654 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 = 3.590351654 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 3.590351654 + 0.625 x = 3.590351654 + 0.625 Combine like terms: 3.590351654 + 0.625 = 4.215351654 x = 4.215351654 Simplifying x = 4.215351654

Subproblem 2

x + -0.625 = -3.590351654 Simplifying x + -0.625 = -3.590351654 Reorder the terms: -0.625 + x = -3.590351654 Solving -0.625 + x = -3.590351654 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 = -3.590351654 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -3.590351654 + 0.625 x = -3.590351654 + 0.625 Combine like terms: -3.590351654 + 0.625 = -2.965351654 x = -2.965351654 Simplifying x = -2.965351654

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.215351654, -2.965351654}

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