0=5x^2-6x-50

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Solution for 0=5x^2-6x-50 equation:


Simplifying
0 = 5x2 + -6x + -50

Reorder the terms:
0 = -50 + -6x + 5x2

Solving
0 = -50 + -6x + 5x2

Solving for variable 'x'.

Combine like terms: 0 + 50 = 50
50 + 6x + -5x2 = -50 + -6x + 5x2 + 50 + 6x + -5x2

Reorder the terms:
50 + 6x + -5x2 = -50 + 50 + -6x + 6x + 5x2 + -5x2

Combine like terms: -50 + 50 = 0
50 + 6x + -5x2 = 0 + -6x + 6x + 5x2 + -5x2
50 + 6x + -5x2 = -6x + 6x + 5x2 + -5x2

Combine like terms: -6x + 6x = 0
50 + 6x + -5x2 = 0 + 5x2 + -5x2
50 + 6x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
50 + 6x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-10 + -1.2x + x2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -1.2x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + -1.2x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1.2x + x2 = 0 + 10
-1.2x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
-1.2x + x2 = 10

The x term is -1.2x.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2x + 0.36 + x2 = 10 + 0.36

Reorder the terms:
0.36 + -1.2x + x2 = 10 + 0.36

Combine like terms: 10 + 0.36 = 10.36
0.36 + -1.2x + x2 = 10.36

Factor a perfect square on the left side:
(x + -0.6)(x + -0.6) = 10.36

Calculate the square root of the right side: 3.218695388

Break this problem into two subproblems by setting 
(x + -0.6) equal to 3.218695388 and -3.218695388.

Subproblem 1

x + -0.6 = 3.218695388 Simplifying x + -0.6 = 3.218695388 Reorder the terms: -0.6 + x = 3.218695388 Solving -0.6 + x = 3.218695388 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 3.218695388 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 3.218695388 + 0.6 x = 3.218695388 + 0.6 Combine like terms: 3.218695388 + 0.6 = 3.818695388 x = 3.818695388 Simplifying x = 3.818695388

Subproblem 2

x + -0.6 = -3.218695388 Simplifying x + -0.6 = -3.218695388 Reorder the terms: -0.6 + x = -3.218695388 Solving -0.6 + x = -3.218695388 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -3.218695388 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -3.218695388 + 0.6 x = -3.218695388 + 0.6 Combine like terms: -3.218695388 + 0.6 = -2.618695388 x = -2.618695388 Simplifying x = -2.618695388

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.818695388, -2.618695388}

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