2x^2-12x=154

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Solution for 2x^2-12x=154 equation:


Simplifying
2x2 + -12x = 154

Reorder the terms:
-12x + 2x2 = 154

Solving
-12x + 2x2 = 154

Solving for variable 'x'.

Reorder the terms:
-154 + -12x + 2x2 = 154 + -154

Combine like terms: 154 + -154 = 0
-154 + -12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-77 + -6x + x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-77 + -6x + x2)' equal to zero and attempt to solve: Simplifying -77 + -6x + x2 = 0 Solving -77 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '77' to each side of the equation. -77 + -6x + 77 + x2 = 0 + 77 Reorder the terms: -77 + 77 + -6x + x2 = 0 + 77 Combine like terms: -77 + 77 = 0 0 + -6x + x2 = 0 + 77 -6x + x2 = 0 + 77 Combine like terms: 0 + 77 = 77 -6x + x2 = 77 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 77 + 9 Reorder the terms: 9 + -6x + x2 = 77 + 9 Combine like terms: 77 + 9 = 86 9 + -6x + x2 = 86 Factor a perfect square on the left side: (x + -3)(x + -3) = 86 Calculate the square root of the right side: 9.273618495 Break this problem into two subproblems by setting (x + -3) equal to 9.273618495 and -9.273618495.

Subproblem 1

x + -3 = 9.273618495 Simplifying x + -3 = 9.273618495 Reorder the terms: -3 + x = 9.273618495 Solving -3 + x = 9.273618495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 9.273618495 + 3 Combine like terms: -3 + 3 = 0 0 + x = 9.273618495 + 3 x = 9.273618495 + 3 Combine like terms: 9.273618495 + 3 = 12.273618495 x = 12.273618495 Simplifying x = 12.273618495

Subproblem 2

x + -3 = -9.273618495 Simplifying x + -3 = -9.273618495 Reorder the terms: -3 + x = -9.273618495 Solving -3 + x = -9.273618495 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -9.273618495 + 3 Combine like terms: -3 + 3 = 0 0 + x = -9.273618495 + 3 x = -9.273618495 + 3 Combine like terms: -9.273618495 + 3 = -6.273618495 x = -6.273618495 Simplifying x = -6.273618495

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.273618495, -6.273618495}

Solution

x = {12.273618495, -6.273618495}

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