125.6=9.42x^2+37.68x

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Solution for 125.6=9.42x^2+37.68x equation:


Simplifying
125.6 = 9.42x2 + 37.68x

Reorder the terms:
125.6 = 37.68x + 9.42x2

Solving
125.6 = 37.68x + 9.42x2

Solving for variable 'x'.

Reorder the terms:
125.6 + -37.68x + -9.42x2 = 37.68x + -37.68x + 9.42x2 + -9.42x2

Combine like terms: 37.68x + -37.68x = 0.00
125.6 + -37.68x + -9.42x2 = 0.00 + 9.42x2 + -9.42x2
125.6 + -37.68x + -9.42x2 = 9.42x2 + -9.42x2

Combine like terms: 9.42x2 + -9.42x2 = 0.00
125.6 + -37.68x + -9.42x2 = 0.00

Begin completing the square.  Divide all terms by
-9.42 the coefficient of the squared term: 

Divide each side by '-9.42'.
-13.33333333 + 4x + x2 = 0

Move the constant term to the right:

Add '13.33333333' to each side of the equation.
-13.33333333 + 4x + 13.33333333 + x2 = 0 + 13.33333333

Reorder the terms:
-13.33333333 + 13.33333333 + 4x + x2 = 0 + 13.33333333

Combine like terms: -13.33333333 + 13.33333333 = 0.00000000
0.00000000 + 4x + x2 = 0 + 13.33333333
4x + x2 = 0 + 13.33333333

Combine like terms: 0 + 13.33333333 = 13.33333333
4x + x2 = 13.33333333

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 13.33333333 + 4

Reorder the terms:
4 + 4x + x2 = 13.33333333 + 4

Combine like terms: 13.33333333 + 4 = 17.33333333
4 + 4x + x2 = 17.33333333

Factor a perfect square on the left side:
(x + 2)(x + 2) = 17.33333333

Calculate the square root of the right side: 4.163331999

Break this problem into two subproblems by setting 
(x + 2) equal to 4.163331999 and -4.163331999.

Subproblem 1

x + 2 = 4.163331999 Simplifying x + 2 = 4.163331999 Reorder the terms: 2 + x = 4.163331999 Solving 2 + x = 4.163331999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 4.163331999 + -2 Combine like terms: 2 + -2 = 0 0 + x = 4.163331999 + -2 x = 4.163331999 + -2 Combine like terms: 4.163331999 + -2 = 2.163331999 x = 2.163331999 Simplifying x = 2.163331999

Subproblem 2

x + 2 = -4.163331999 Simplifying x + 2 = -4.163331999 Reorder the terms: 2 + x = -4.163331999 Solving 2 + x = -4.163331999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -4.163331999 + -2 Combine like terms: 2 + -2 = 0 0 + x = -4.163331999 + -2 x = -4.163331999 + -2 Combine like terms: -4.163331999 + -2 = -6.163331999 x = -6.163331999 Simplifying x = -6.163331999

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.163331999, -6.163331999}

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