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Simplifying 0 = 12(x2 + -9x + -56) Reorder the terms: 0 = 12(-56 + -9x + x2) 0 = (-56 * 12 + -9x * 12 + x2 * 12) 0 = (-672 + -108x + 12x2) Solving 0 = -672 + -108x + 12x2 Solving for variable 'x'. Combine like terms: 0 + 672 = 672 672 + 108x + -12x2 = -672 + -108x + 12x2 + 672 + 108x + -12x2 Reorder the terms: 672 + 108x + -12x2 = -672 + 672 + -108x + 108x + 12x2 + -12x2 Combine like terms: -672 + 672 = 0 672 + 108x + -12x2 = 0 + -108x + 108x + 12x2 + -12x2 672 + 108x + -12x2 = -108x + 108x + 12x2 + -12x2 Combine like terms: -108x + 108x = 0 672 + 108x + -12x2 = 0 + 12x2 + -12x2 672 + 108x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 672 + 108x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '12'. 12(56 + 9x + -1x2) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(56 + 9x + -1x2)' equal to zero and attempt to solve: Simplifying 56 + 9x + -1x2 = 0 Solving 56 + 9x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -56 + -9x + x2 = 0 Move the constant term to the right: Add '56' to each side of the equation. -56 + -9x + 56 + x2 = 0 + 56 Reorder the terms: -56 + 56 + -9x + x2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + -9x + x2 = 0 + 56 -9x + x2 = 0 + 56 Combine like terms: 0 + 56 = 56 -9x + x2 = 56 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 = 56 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 56 + 20.25 Combine like terms: 56 + 20.25 = 76.25 20.25 + -9x + x2 = 76.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 76.25 Calculate the square root of the right side: 8.732124598 Break this problem into two subproblems by setting (x + -4.5) equal to 8.732124598 and -8.732124598.Subproblem 1
x + -4.5 = 8.732124598 Simplifying x + -4.5 = 8.732124598 Reorder the terms: -4.5 + x = 8.732124598 Solving -4.5 + x = 8.732124598 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 = 8.732124598 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 8.732124598 + 4.5 x = 8.732124598 + 4.5 Combine like terms: 8.732124598 + 4.5 = 13.232124598 x = 13.232124598 Simplifying x = 13.232124598Subproblem 2
x + -4.5 = -8.732124598 Simplifying x + -4.5 = -8.732124598 Reorder the terms: -4.5 + x = -8.732124598 Solving -4.5 + x = -8.732124598 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 = -8.732124598 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -8.732124598 + 4.5 x = -8.732124598 + 4.5 Combine like terms: -8.732124598 + 4.5 = -4.232124598 x = -4.232124598 Simplifying x = -4.232124598Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.232124598, -4.232124598}Solution
x = {13.232124598, -4.232124598}
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