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Simplifying 6x2 + 54x + -648 = 0 Reorder the terms: -648 + 54x + 6x2 = 0 Solving -648 + 54x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-108 + 9x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-108 + 9x + x2)' equal to zero and attempt to solve: Simplifying -108 + 9x + x2 = 0 Solving -108 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '108' to each side of the equation. -108 + 9x + 108 + x2 = 0 + 108 Reorder the terms: -108 + 108 + 9x + x2 = 0 + 108 Combine like terms: -108 + 108 = 0 0 + 9x + x2 = 0 + 108 9x + x2 = 0 + 108 Combine like terms: 0 + 108 = 108 9x + x2 = 108 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 108 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 108 + 20.25 Combine like terms: 108 + 20.25 = 128.25 20.25 + 9x + x2 = 128.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 128.25 Calculate the square root of the right side: 11.324751653 Break this problem into two subproblems by setting (x + 4.5) equal to 11.324751653 and -11.324751653.Subproblem 1
x + 4.5 = 11.324751653 Simplifying x + 4.5 = 11.324751653 Reorder the terms: 4.5 + x = 11.324751653 Solving 4.5 + x = 11.324751653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 11.324751653 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 11.324751653 + -4.5 x = 11.324751653 + -4.5 Combine like terms: 11.324751653 + -4.5 = 6.824751653 x = 6.824751653 Simplifying x = 6.824751653Subproblem 2
x + 4.5 = -11.324751653 Simplifying x + 4.5 = -11.324751653 Reorder the terms: 4.5 + x = -11.324751653 Solving 4.5 + x = -11.324751653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -11.324751653 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -11.324751653 + -4.5 x = -11.324751653 + -4.5 Combine like terms: -11.324751653 + -4.5 = -15.824751653 x = -15.824751653 Simplifying x = -15.824751653Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.824751653, -15.824751653}Solution
x = {6.824751653, -15.824751653}
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