2x^2-30x+9=-12

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Solution for 2x^2-30x+9=-12 equation:


Simplifying
2x2 + -30x + 9 = -12

Reorder the terms:
9 + -30x + 2x2 = -12

Solving
9 + -30x + 2x2 = -12

Solving for variable 'x'.

Reorder the terms:
9 + 12 + -30x + 2x2 = -12 + 12

Combine like terms: 9 + 12 = 21
21 + -30x + 2x2 = -12 + 12

Combine like terms: -12 + 12 = 0
21 + -30x + 2x2 = 0

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

Divide each side by '2'.
10.5 + -15x + x2 = 0

Move the constant term to the right:

Add '-10.5' to each side of the equation.
10.5 + -15x + -10.5 + x2 = 0 + -10.5

Reorder the terms:
10.5 + -10.5 + -15x + x2 = 0 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + -15x + x2 = 0 + -10.5
-15x + x2 = 0 + -10.5

Combine like terms: 0 + -10.5 = -10.5
-15x + x2 = -10.5

The x term is -15x.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15x + 56.25 + x2 = -10.5 + 56.25

Reorder the terms:
56.25 + -15x + x2 = -10.5 + 56.25

Combine like terms: -10.5 + 56.25 = 45.75
56.25 + -15x + x2 = 45.75

Factor a perfect square on the left side:
(x + -7.5)(x + -7.5) = 45.75

Calculate the square root of the right side: 6.763874629

Break this problem into two subproblems by setting 
(x + -7.5) equal to 6.763874629 and -6.763874629.

Subproblem 1

x + -7.5 = 6.763874629 Simplifying x + -7.5 = 6.763874629 Reorder the terms: -7.5 + x = 6.763874629 Solving -7.5 + x = 6.763874629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 6.763874629 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 6.763874629 + 7.5 x = 6.763874629 + 7.5 Combine like terms: 6.763874629 + 7.5 = 14.263874629 x = 14.263874629 Simplifying x = 14.263874629

Subproblem 2

x + -7.5 = -6.763874629 Simplifying x + -7.5 = -6.763874629 Reorder the terms: -7.5 + x = -6.763874629 Solving -7.5 + x = -6.763874629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -6.763874629 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -6.763874629 + 7.5 x = -6.763874629 + 7.5 Combine like terms: -6.763874629 + 7.5 = 0.736125371 x = 0.736125371 Simplifying x = 0.736125371

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.263874629, 0.736125371}

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