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Simplifying 9x3 + 56x2 + -12x = 0 Reorder the terms: -12x + 56x2 + 9x3 = 0 Solving -12x + 56x2 + 9x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-12 + 56x + 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 '(-12 + 56x + 9x2)' equal to zero and attempt to solve: Simplifying -12 + 56x + 9x2 = 0 Solving -12 + 56x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.333333333 + 6.222222222x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + 6.222222222x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + 6.222222222x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + 6.222222222x + x2 = 0 + 1.333333333 6.222222222x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 6.222222222x + x2 = 1.333333333 The x term is 6.222222222x. Take half its coefficient (3.111111111). Square it (9.679012345) and add it to both sides. Add '9.679012345' to each side of the equation. 6.222222222x + 9.679012345 + x2 = 1.333333333 + 9.679012345 Reorder the terms: 9.679012345 + 6.222222222x + x2 = 1.333333333 + 9.679012345 Combine like terms: 1.333333333 + 9.679012345 = 11.012345678 9.679012345 + 6.222222222x + x2 = 11.012345678 Factor a perfect square on the left side: (x + 3.111111111)(x + 3.111111111) = 11.012345678 Calculate the square root of the right side: 3.318485449 Break this problem into two subproblems by setting (x + 3.111111111) equal to 3.318485449 and -3.318485449.Subproblem 1
x + 3.111111111 = 3.318485449 Simplifying x + 3.111111111 = 3.318485449 Reorder the terms: 3.111111111 + x = 3.318485449 Solving 3.111111111 + x = 3.318485449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.111111111' to each side of the equation. 3.111111111 + -3.111111111 + x = 3.318485449 + -3.111111111 Combine like terms: 3.111111111 + -3.111111111 = 0.000000000 0.000000000 + x = 3.318485449 + -3.111111111 x = 3.318485449 + -3.111111111 Combine like terms: 3.318485449 + -3.111111111 = 0.207374338 x = 0.207374338 Simplifying x = 0.207374338Subproblem 2
x + 3.111111111 = -3.318485449 Simplifying x + 3.111111111 = -3.318485449 Reorder the terms: 3.111111111 + x = -3.318485449 Solving 3.111111111 + x = -3.318485449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.111111111' to each side of the equation. 3.111111111 + -3.111111111 + x = -3.318485449 + -3.111111111 Combine like terms: 3.111111111 + -3.111111111 = 0.000000000 0.000000000 + x = -3.318485449 + -3.111111111 x = -3.318485449 + -3.111111111 Combine like terms: -3.318485449 + -3.111111111 = -6.42959656 x = -6.42959656 Simplifying x = -6.42959656Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.207374338, -6.42959656}Solution
x = {0, 0.207374338, -6.42959656}
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