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Simplifying 2x2 + -12x + -108 = 0 Reorder the terms: -108 + -12x + 2x2 = 0 Solving -108 + -12x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-54 + -6x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-54 + -6x + x2)' equal to zero and attempt to solve: Simplifying -54 + -6x + x2 = 0 Solving -54 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '54' to each side of the equation. -54 + -6x + 54 + x2 = 0 + 54 Reorder the terms: -54 + 54 + -6x + x2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + -6x + x2 = 0 + 54 -6x + x2 = 0 + 54 Combine like terms: 0 + 54 = 54 -6x + x2 = 54 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 = 54 + 9 Reorder the terms: 9 + -6x + x2 = 54 + 9 Combine like terms: 54 + 9 = 63 9 + -6x + x2 = 63 Factor a perfect square on the left side: (x + -3)(x + -3) = 63 Calculate the square root of the right side: 7.937253933 Break this problem into two subproblems by setting (x + -3) equal to 7.937253933 and -7.937253933.Subproblem 1
x + -3 = 7.937253933 Simplifying x + -3 = 7.937253933 Reorder the terms: -3 + x = 7.937253933 Solving -3 + x = 7.937253933 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 = 7.937253933 + 3 Combine like terms: -3 + 3 = 0 0 + x = 7.937253933 + 3 x = 7.937253933 + 3 Combine like terms: 7.937253933 + 3 = 10.937253933 x = 10.937253933 Simplifying x = 10.937253933Subproblem 2
x + -3 = -7.937253933 Simplifying x + -3 = -7.937253933 Reorder the terms: -3 + x = -7.937253933 Solving -3 + x = -7.937253933 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 = -7.937253933 + 3 Combine like terms: -3 + 3 = 0 0 + x = -7.937253933 + 3 x = -7.937253933 + 3 Combine like terms: -7.937253933 + 3 = -4.937253933 x = -4.937253933 Simplifying x = -4.937253933Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.937253933, -4.937253933}Solution
x = {10.937253933, -4.937253933}
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