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Simplifying 72x + 15x2 + -1x3 = 0 Solving 72x + 15x2 + -1x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(72 + 15x + -1x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(72 + 15x + -1x2)' equal to zero and attempt to solve: Simplifying 72 + 15x + -1x2 = 0 Solving 72 + 15x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -72 + -15x + x2 = 0 Move the constant term to the right: Add '72' to each side of the equation. -72 + -15x + 72 + x2 = 0 + 72 Reorder the terms: -72 + 72 + -15x + x2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + -15x + x2 = 0 + 72 -15x + x2 = 0 + 72 Combine like terms: 0 + 72 = 72 -15x + x2 = 72 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = 72 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 72 + 56.25 Combine like terms: 72 + 56.25 = 128.25 56.25 + -15x + x2 = 128.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 128.25 Calculate the square root of the right side: 11.324751653 Break this problem into two subproblems by setting (x + -7.5) equal to 11.324751653 and -11.324751653.Subproblem 1
x + -7.5 = 11.324751653 Simplifying x + -7.5 = 11.324751653 Reorder the terms: -7.5 + x = 11.324751653 Solving -7.5 + x = 11.324751653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 11.324751653 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 11.324751653 + 7.5 x = 11.324751653 + 7.5 Combine like terms: 11.324751653 + 7.5 = 18.824751653 x = 18.824751653 Simplifying x = 18.824751653Subproblem 2
x + -7.5 = -11.324751653 Simplifying x + -7.5 = -11.324751653 Reorder the terms: -7.5 + x = -11.324751653 Solving -7.5 + x = -11.324751653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -11.324751653 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -11.324751653 + 7.5 x = -11.324751653 + 7.5 Combine like terms: -11.324751653 + 7.5 = -3.824751653 x = -3.824751653 Simplifying x = -3.824751653Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.824751653, -3.824751653}Solution
x = {0, 18.824751653, -3.824751653}
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