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Simplifying 2x2 + -24x + -54 = 0 Reorder the terms: -54 + -24x + 2x2 = 0 Solving -54 + -24x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-27 + -12x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-27 + -12x + x2)' equal to zero and attempt to solve: Simplifying -27 + -12x + x2 = 0 Solving -27 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + -12x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + -12x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -12x + x2 = 0 + 27 -12x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 -12x + x2 = 27 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 = 27 + 36 Reorder the terms: 36 + -12x + x2 = 27 + 36 Combine like terms: 27 + 36 = 63 36 + -12x + x2 = 63 Factor a perfect square on the left side: (x + -6)(x + -6) = 63 Calculate the square root of the right side: 7.937253933 Break this problem into two subproblems by setting (x + -6) equal to 7.937253933 and -7.937253933.Subproblem 1
x + -6 = 7.937253933 Simplifying x + -6 = 7.937253933 Reorder the terms: -6 + x = 7.937253933 Solving -6 + x = 7.937253933 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 = 7.937253933 + 6 Combine like terms: -6 + 6 = 0 0 + x = 7.937253933 + 6 x = 7.937253933 + 6 Combine like terms: 7.937253933 + 6 = 13.937253933 x = 13.937253933 Simplifying x = 13.937253933Subproblem 2
x + -6 = -7.937253933 Simplifying x + -6 = -7.937253933 Reorder the terms: -6 + x = -7.937253933 Solving -6 + x = -7.937253933 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 = -7.937253933 + 6 Combine like terms: -6 + 6 = 0 0 + x = -7.937253933 + 6 x = -7.937253933 + 6 Combine like terms: -7.937253933 + 6 = -1.937253933 x = -1.937253933 Simplifying x = -1.937253933Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.937253933, -1.937253933}Solution
x = {13.937253933, -1.937253933}
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