2x^2+36x-12=0

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Solution for 2x^2+36x-12=0 equation:


Simplifying
2x2 + 36x + -12 = 0

Reorder the terms:
-12 + 36x + 2x2 = 0

Solving
-12 + 36x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 18x + x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-6 + 18x + x2)' equal to zero and attempt to solve: Simplifying -6 + 18x + x2 = 0 Solving -6 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 18x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 18x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 18x + x2 = 0 + 6 18x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 18x + x2 = 6 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = 6 + 81 Reorder the terms: 81 + 18x + x2 = 6 + 81 Combine like terms: 6 + 81 = 87 81 + 18x + x2 = 87 Factor a perfect square on the left side: (x + 9)(x + 9) = 87 Calculate the square root of the right side: 9.327379053 Break this problem into two subproblems by setting (x + 9) equal to 9.327379053 and -9.327379053.

Subproblem 1

x + 9 = 9.327379053 Simplifying x + 9 = 9.327379053 Reorder the terms: 9 + x = 9.327379053 Solving 9 + x = 9.327379053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 9.327379053 + -9 Combine like terms: 9 + -9 = 0 0 + x = 9.327379053 + -9 x = 9.327379053 + -9 Combine like terms: 9.327379053 + -9 = 0.327379053 x = 0.327379053 Simplifying x = 0.327379053

Subproblem 2

x + 9 = -9.327379053 Simplifying x + 9 = -9.327379053 Reorder the terms: 9 + x = -9.327379053 Solving 9 + x = -9.327379053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -9.327379053 + -9 Combine like terms: 9 + -9 = 0 0 + x = -9.327379053 + -9 x = -9.327379053 + -9 Combine like terms: -9.327379053 + -9 = -18.327379053 x = -18.327379053 Simplifying x = -18.327379053

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.327379053, -18.327379053}

Solution

x = {0.327379053, -18.327379053}

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