5x^2+6x-13=41-31x

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Solution for 5x^2+6x-13=41-31x equation:


Simplifying
5x2 + 6x + -13 = 41 + -31x

Reorder the terms:
-13 + 6x + 5x2 = 41 + -31x

Solving
-13 + 6x + 5x2 = 41 + -31x

Solving for variable 'x'.

Reorder the terms:
-13 + -41 + 6x + 31x + 5x2 = 41 + -31x + -41 + 31x

Combine like terms: -13 + -41 = -54
-54 + 6x + 31x + 5x2 = 41 + -31x + -41 + 31x

Combine like terms: 6x + 31x = 37x
-54 + 37x + 5x2 = 41 + -31x + -41 + 31x

Reorder the terms:
-54 + 37x + 5x2 = 41 + -41 + -31x + 31x

Combine like terms: 41 + -41 = 0
-54 + 37x + 5x2 = 0 + -31x + 31x
-54 + 37x + 5x2 = -31x + 31x

Combine like terms: -31x + 31x = 0
-54 + 37x + 5x2 = 0

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

Divide each side by '5'.
-10.8 + 7.4x + x2 = 0

Move the constant term to the right:

Add '10.8' to each side of the equation.
-10.8 + 7.4x + 10.8 + x2 = 0 + 10.8

Reorder the terms:
-10.8 + 10.8 + 7.4x + x2 = 0 + 10.8

Combine like terms: -10.8 + 10.8 = 0.0
0.0 + 7.4x + x2 = 0 + 10.8
7.4x + x2 = 0 + 10.8

Combine like terms: 0 + 10.8 = 10.8
7.4x + x2 = 10.8

The x term is 7.4x.  Take half its coefficient (3.7).
Square it (13.69) and add it to both sides.

Add '13.69' to each side of the equation.
7.4x + 13.69 + x2 = 10.8 + 13.69

Reorder the terms:
13.69 + 7.4x + x2 = 10.8 + 13.69

Combine like terms: 10.8 + 13.69 = 24.49
13.69 + 7.4x + x2 = 24.49

Factor a perfect square on the left side:
(x + 3.7)(x + 3.7) = 24.49

Calculate the square root of the right side: 4.948737213

Break this problem into two subproblems by setting 
(x + 3.7) equal to 4.948737213 and -4.948737213.

Subproblem 1

x + 3.7 = 4.948737213 Simplifying x + 3.7 = 4.948737213 Reorder the terms: 3.7 + x = 4.948737213 Solving 3.7 + x = 4.948737213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.7' to each side of the equation. 3.7 + -3.7 + x = 4.948737213 + -3.7 Combine like terms: 3.7 + -3.7 = 0.0 0.0 + x = 4.948737213 + -3.7 x = 4.948737213 + -3.7 Combine like terms: 4.948737213 + -3.7 = 1.248737213 x = 1.248737213 Simplifying x = 1.248737213

Subproblem 2

x + 3.7 = -4.948737213 Simplifying x + 3.7 = -4.948737213 Reorder the terms: 3.7 + x = -4.948737213 Solving 3.7 + x = -4.948737213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.7' to each side of the equation. 3.7 + -3.7 + x = -4.948737213 + -3.7 Combine like terms: 3.7 + -3.7 = 0.0 0.0 + x = -4.948737213 + -3.7 x = -4.948737213 + -3.7 Combine like terms: -4.948737213 + -3.7 = -8.648737213 x = -8.648737213 Simplifying x = -8.648737213

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.248737213, -8.648737213}

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