5x^2-46x-36=0

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Solution for 5x^2-46x-36=0 equation:


Simplifying
5x2 + -46x + -36 = 0

Reorder the terms:
-36 + -46x + 5x2 = 0

Solving
-36 + -46x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-7.2 + -9.2x + x2 = 0

Move the constant term to the right:

Add '7.2' to each side of the equation.
-7.2 + -9.2x + 7.2 + x2 = 0 + 7.2

Reorder the terms:
-7.2 + 7.2 + -9.2x + x2 = 0 + 7.2

Combine like terms: -7.2 + 7.2 = 0.0
0.0 + -9.2x + x2 = 0 + 7.2
-9.2x + x2 = 0 + 7.2

Combine like terms: 0 + 7.2 = 7.2
-9.2x + x2 = 7.2

The x term is -9.2x.  Take half its coefficient (-4.6).
Square it (21.16) and add it to both sides.

Add '21.16' to each side of the equation.
-9.2x + 21.16 + x2 = 7.2 + 21.16

Reorder the terms:
21.16 + -9.2x + x2 = 7.2 + 21.16

Combine like terms: 7.2 + 21.16 = 28.36
21.16 + -9.2x + x2 = 28.36

Factor a perfect square on the left side:
(x + -4.6)(x + -4.6) = 28.36

Calculate the square root of the right side: 5.325410782

Break this problem into two subproblems by setting 
(x + -4.6) equal to 5.325410782 and -5.325410782.

Subproblem 1

x + -4.6 = 5.325410782 Simplifying x + -4.6 = 5.325410782 Reorder the terms: -4.6 + x = 5.325410782 Solving -4.6 + x = 5.325410782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.6' to each side of the equation. -4.6 + 4.6 + x = 5.325410782 + 4.6 Combine like terms: -4.6 + 4.6 = 0.0 0.0 + x = 5.325410782 + 4.6 x = 5.325410782 + 4.6 Combine like terms: 5.325410782 + 4.6 = 9.925410782 x = 9.925410782 Simplifying x = 9.925410782

Subproblem 2

x + -4.6 = -5.325410782 Simplifying x + -4.6 = -5.325410782 Reorder the terms: -4.6 + x = -5.325410782 Solving -4.6 + x = -5.325410782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.6' to each side of the equation. -4.6 + 4.6 + x = -5.325410782 + 4.6 Combine like terms: -4.6 + 4.6 = 0.0 0.0 + x = -5.325410782 + 4.6 x = -5.325410782 + 4.6 Combine like terms: -5.325410782 + 4.6 = -0.725410782 x = -0.725410782 Simplifying x = -0.725410782

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.925410782, -0.725410782}

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