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Simplifying 182 + -108x + 12x2 = 0 Solving 182 + -108x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(91 + -54x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(91 + -54x + 6x2)' equal to zero and attempt to solve: Simplifying 91 + -54x + 6x2 = 0 Solving 91 + -54x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 15.16666667 + -9x + x2 = 0 Move the constant term to the right: Add '-15.16666667' to each side of the equation. 15.16666667 + -9x + -15.16666667 + x2 = 0 + -15.16666667 Reorder the terms: 15.16666667 + -15.16666667 + -9x + x2 = 0 + -15.16666667 Combine like terms: 15.16666667 + -15.16666667 = 0.00000000 0.00000000 + -9x + x2 = 0 + -15.16666667 -9x + x2 = 0 + -15.16666667 Combine like terms: 0 + -15.16666667 = -15.16666667 -9x + x2 = -15.16666667 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 = -15.16666667 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -15.16666667 + 20.25 Combine like terms: -15.16666667 + 20.25 = 5.08333333 20.25 + -9x + x2 = 5.08333333 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 5.08333333 Calculate the square root of the right side: 2.254624876 Break this problem into two subproblems by setting (x + -4.5) equal to 2.254624876 and -2.254624876.Subproblem 1
x + -4.5 = 2.254624876 Simplifying x + -4.5 = 2.254624876 Reorder the terms: -4.5 + x = 2.254624876 Solving -4.5 + x = 2.254624876 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 = 2.254624876 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 2.254624876 + 4.5 x = 2.254624876 + 4.5 Combine like terms: 2.254624876 + 4.5 = 6.754624876 x = 6.754624876 Simplifying x = 6.754624876Subproblem 2
x + -4.5 = -2.254624876 Simplifying x + -4.5 = -2.254624876 Reorder the terms: -4.5 + x = -2.254624876 Solving -4.5 + x = -2.254624876 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 = -2.254624876 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -2.254624876 + 4.5 x = -2.254624876 + 4.5 Combine like terms: -2.254624876 + 4.5 = 2.245375124 x = 2.245375124 Simplifying x = 2.245375124Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.754624876, 2.245375124}Solution
x = {6.754624876, 2.245375124}
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