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Simplifying 6x2 + -12x + -108 = 0 Reorder the terms: -108 + -12x + 6x2 = 0 Solving -108 + -12x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-18 + -2x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-18 + -2x + x2)' equal to zero and attempt to solve: Simplifying -18 + -2x + x2 = 0 Solving -18 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + -2x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + -2x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -2x + x2 = 0 + 18 -2x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 -2x + x2 = 18 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 18 + 1 Reorder the terms: 1 + -2x + x2 = 18 + 1 Combine like terms: 18 + 1 = 19 1 + -2x + x2 = 19 Factor a perfect square on the left side: (x + -1)(x + -1) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (x + -1) equal to 4.358898944 and -4.358898944.Subproblem 1
x + -1 = 4.358898944 Simplifying x + -1 = 4.358898944 Reorder the terms: -1 + x = 4.358898944 Solving -1 + x = 4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 4.358898944 + 1 Combine like terms: -1 + 1 = 0 0 + x = 4.358898944 + 1 x = 4.358898944 + 1 Combine like terms: 4.358898944 + 1 = 5.358898944 x = 5.358898944 Simplifying x = 5.358898944Subproblem 2
x + -1 = -4.358898944 Simplifying x + -1 = -4.358898944 Reorder the terms: -1 + x = -4.358898944 Solving -1 + x = -4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -4.358898944 + 1 Combine like terms: -1 + 1 = 0 0 + x = -4.358898944 + 1 x = -4.358898944 + 1 Combine like terms: -4.358898944 + 1 = -3.358898944 x = -3.358898944 Simplifying x = -3.358898944Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.358898944, -3.358898944}Solution
x = {5.358898944, -3.358898944}
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