21.33x^2+20x-133.33=12x^2

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Solution for 21.33x^2+20x-133.33=12x^2 equation:


Simplifying
21.33x2 + 20x + -133.33 = 12x2

Reorder the terms:
-133.33 + 20x + 21.33x2 = 12x2

Solving
-133.33 + 20x + 21.33x2 = 12x2

Solving for variable 'x'.

Combine like terms: 21.33x2 + -12x2 = 9.33x2
-133.33 + 20x + 9.33x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
-133.33 + 20x + 9.33x2 = 0

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

Divide each side by '9.33'.
-14.29046088 + 2.143622722x + x2 = 0

Move the constant term to the right:

Add '14.29046088' to each side of the equation.
-14.29046088 + 2.143622722x + 14.29046088 + x2 = 0 + 14.29046088

Reorder the terms:
-14.29046088 + 14.29046088 + 2.143622722x + x2 = 0 + 14.29046088

Combine like terms: -14.29046088 + 14.29046088 = 0.00000000
0.00000000 + 2.143622722x + x2 = 0 + 14.29046088
2.143622722x + x2 = 0 + 14.29046088

Combine like terms: 0 + 14.29046088 = 14.29046088
2.143622722x + x2 = 14.29046088

The x term is 2.143622722x.  Take half its coefficient (1.071811361).
Square it (1.148779594) and add it to both sides.

Add '1.148779594' to each side of the equation.
2.143622722x + 1.148779594 + x2 = 14.29046088 + 1.148779594

Reorder the terms:
1.148779594 + 2.143622722x + x2 = 14.29046088 + 1.148779594

Combine like terms: 14.29046088 + 1.148779594 = 15.439240474
1.148779594 + 2.143622722x + x2 = 15.439240474

Factor a perfect square on the left side:
(x + 1.071811361)(x + 1.071811361) = 15.439240474

Calculate the square root of the right side: 3.929279893

Break this problem into two subproblems by setting 
(x + 1.071811361) equal to 3.929279893 and -3.929279893.

Subproblem 1

x + 1.071811361 = 3.929279893 Simplifying x + 1.071811361 = 3.929279893 Reorder the terms: 1.071811361 + x = 3.929279893 Solving 1.071811361 + x = 3.929279893 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.071811361' to each side of the equation. 1.071811361 + -1.071811361 + x = 3.929279893 + -1.071811361 Combine like terms: 1.071811361 + -1.071811361 = 0.000000000 0.000000000 + x = 3.929279893 + -1.071811361 x = 3.929279893 + -1.071811361 Combine like terms: 3.929279893 + -1.071811361 = 2.857468532 x = 2.857468532 Simplifying x = 2.857468532

Subproblem 2

x + 1.071811361 = -3.929279893 Simplifying x + 1.071811361 = -3.929279893 Reorder the terms: 1.071811361 + x = -3.929279893 Solving 1.071811361 + x = -3.929279893 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.071811361' to each side of the equation. 1.071811361 + -1.071811361 + x = -3.929279893 + -1.071811361 Combine like terms: 1.071811361 + -1.071811361 = 0.000000000 0.000000000 + x = -3.929279893 + -1.071811361 x = -3.929279893 + -1.071811361 Combine like terms: -3.929279893 + -1.071811361 = -5.001091254 x = -5.001091254 Simplifying x = -5.001091254

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.857468532, -5.001091254}

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