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Simplifying 2x2 + -24x = 108 Reorder the terms: -24x + 2x2 = 108 Solving -24x + 2x2 = 108 Solving for variable 'x'. Reorder the terms: -108 + -24x + 2x2 = 108 + -108 Combine like terms: 108 + -108 = 0 -108 + -24x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-54 + -12x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-54 + -12x + x2)' equal to zero and attempt to solve: Simplifying -54 + -12x + x2 = 0 Solving -54 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '54' to each side of the equation. -54 + -12x + 54 + x2 = 0 + 54 Reorder the terms: -54 + 54 + -12x + x2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + -12x + x2 = 0 + 54 -12x + x2 = 0 + 54 Combine like terms: 0 + 54 = 54 -12x + x2 = 54 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 54 + 36 Reorder the terms: 36 + -12x + x2 = 54 + 36 Combine like terms: 54 + 36 = 90 36 + -12x + x2 = 90 Factor a perfect square on the left side: (x + -6)(x + -6) = 90 Calculate the square root of the right side: 9.486832981 Break this problem into two subproblems by setting (x + -6) equal to 9.486832981 and -9.486832981.Subproblem 1
x + -6 = 9.486832981 Simplifying x + -6 = 9.486832981 Reorder the terms: -6 + x = 9.486832981 Solving -6 + x = 9.486832981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 9.486832981 + 6 Combine like terms: -6 + 6 = 0 0 + x = 9.486832981 + 6 x = 9.486832981 + 6 Combine like terms: 9.486832981 + 6 = 15.486832981 x = 15.486832981 Simplifying x = 15.486832981Subproblem 2
x + -6 = -9.486832981 Simplifying x + -6 = -9.486832981 Reorder the terms: -6 + x = -9.486832981 Solving -6 + x = -9.486832981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -9.486832981 + 6 Combine like terms: -6 + 6 = 0 0 + x = -9.486832981 + 6 x = -9.486832981 + 6 Combine like terms: -9.486832981 + 6 = -3.486832981 x = -3.486832981 Simplifying x = -3.486832981Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.486832981, -3.486832981}Solution
x = {15.486832981, -3.486832981}
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