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Simplifying 9x3 + -64x2 + 64x = 0 Reorder the terms: 64x + -64x2 + 9x3 = 0 Solving 64x + -64x2 + 9x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(64 + -64x + 9x2) = 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 '(64 + -64x + 9x2)' equal to zero and attempt to solve: Simplifying 64 + -64x + 9x2 = 0 Solving 64 + -64x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 7.111111111 + -7.111111111x + x2 = 0 Move the constant term to the right: Add '-7.111111111' to each side of the equation. 7.111111111 + -7.111111111x + -7.111111111 + x2 = 0 + -7.111111111 Reorder the terms: 7.111111111 + -7.111111111 + -7.111111111x + x2 = 0 + -7.111111111 Combine like terms: 7.111111111 + -7.111111111 = 0.000000000 0.000000000 + -7.111111111x + x2 = 0 + -7.111111111 -7.111111111x + x2 = 0 + -7.111111111 Combine like terms: 0 + -7.111111111 = -7.111111111 -7.111111111x + x2 = -7.111111111 The x term is -7.111111111x. Take half its coefficient (-3.555555556). Square it (12.64197531) and add it to both sides. Add '12.64197531' to each side of the equation. -7.111111111x + 12.64197531 + x2 = -7.111111111 + 12.64197531 Reorder the terms: 12.64197531 + -7.111111111x + x2 = -7.111111111 + 12.64197531 Combine like terms: -7.111111111 + 12.64197531 = 5.530864199 12.64197531 + -7.111111111x + x2 = 5.530864199 Factor a perfect square on the left side: (x + -3.555555556)(x + -3.555555556) = 5.530864199 Calculate the square root of the right side: 2.351778943 Break this problem into two subproblems by setting (x + -3.555555556) equal to 2.351778943 and -2.351778943.Subproblem 1
x + -3.555555556 = 2.351778943 Simplifying x + -3.555555556 = 2.351778943 Reorder the terms: -3.555555556 + x = 2.351778943 Solving -3.555555556 + x = 2.351778943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.555555556' to each side of the equation. -3.555555556 + 3.555555556 + x = 2.351778943 + 3.555555556 Combine like terms: -3.555555556 + 3.555555556 = 0.000000000 0.000000000 + x = 2.351778943 + 3.555555556 x = 2.351778943 + 3.555555556 Combine like terms: 2.351778943 + 3.555555556 = 5.907334499 x = 5.907334499 Simplifying x = 5.907334499Subproblem 2
x + -3.555555556 = -2.351778943 Simplifying x + -3.555555556 = -2.351778943 Reorder the terms: -3.555555556 + x = -2.351778943 Solving -3.555555556 + x = -2.351778943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.555555556' to each side of the equation. -3.555555556 + 3.555555556 + x = -2.351778943 + 3.555555556 Combine like terms: -3.555555556 + 3.555555556 = 0.000000000 0.000000000 + x = -2.351778943 + 3.555555556 x = -2.351778943 + 3.555555556 Combine like terms: -2.351778943 + 3.555555556 = 1.203776613 x = 1.203776613 Simplifying x = 1.203776613Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.907334499, 1.203776613}Solution
x = {0, 5.907334499, 1.203776613}
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