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Simplifying 27x2 + -312x + -72 = 0 Reorder the terms: -72 + -312x + 27x2 = 0 Solving -72 + -312x + 27x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-24 + -104x + 9x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-24 + -104x + 9x2)' equal to zero and attempt to solve: Simplifying -24 + -104x + 9x2 = 0 Solving -24 + -104x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.666666667 + -11.55555556x + x2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + -11.55555556x + 2.666666667 + x2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + -11.55555556x + x2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + -11.55555556x + x2 = 0 + 2.666666667 -11.55555556x + x2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 -11.55555556x + x2 = 2.666666667 The x term is -11.55555556x. Take half its coefficient (-5.77777778). Square it (33.38271608) and add it to both sides. Add '33.38271608' to each side of the equation. -11.55555556x + 33.38271608 + x2 = 2.666666667 + 33.38271608 Reorder the terms: 33.38271608 + -11.55555556x + x2 = 2.666666667 + 33.38271608 Combine like terms: 2.666666667 + 33.38271608 = 36.049382747 33.38271608 + -11.55555556x + x2 = 36.049382747 Factor a perfect square on the left side: (x + -5.77777778)(x + -5.77777778) = 36.049382747 Calculate the square root of the right side: 6.004113819 Break this problem into two subproblems by setting (x + -5.77777778) equal to 6.004113819 and -6.004113819.Subproblem 1
x + -5.77777778 = 6.004113819 Simplifying x + -5.77777778 = 6.004113819 Reorder the terms: -5.77777778 + x = 6.004113819 Solving -5.77777778 + x = 6.004113819 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.77777778' to each side of the equation. -5.77777778 + 5.77777778 + x = 6.004113819 + 5.77777778 Combine like terms: -5.77777778 + 5.77777778 = 0.00000000 0.00000000 + x = 6.004113819 + 5.77777778 x = 6.004113819 + 5.77777778 Combine like terms: 6.004113819 + 5.77777778 = 11.781891599 x = 11.781891599 Simplifying x = 11.781891599Subproblem 2
x + -5.77777778 = -6.004113819 Simplifying x + -5.77777778 = -6.004113819 Reorder the terms: -5.77777778 + x = -6.004113819 Solving -5.77777778 + x = -6.004113819 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.77777778' to each side of the equation. -5.77777778 + 5.77777778 + x = -6.004113819 + 5.77777778 Combine like terms: -5.77777778 + 5.77777778 = 0.00000000 0.00000000 + x = -6.004113819 + 5.77777778 x = -6.004113819 + 5.77777778 Combine like terms: -6.004113819 + 5.77777778 = -0.226336039 x = -0.226336039 Simplifying x = -0.226336039Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.781891599, -0.226336039}Solution
x = {11.781891599, -0.226336039}
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