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Simplifying 12x2 + -116x + 208 = 0 Reorder the terms: 208 + -116x + 12x2 = 0 Solving 208 + -116x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(52 + -29x + 3x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(52 + -29x + 3x2)' equal to zero and attempt to solve: Simplifying 52 + -29x + 3x2 = 0 Solving 52 + -29x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 17.33333333 + -9.666666667x + x2 = 0 Move the constant term to the right: Add '-17.33333333' to each side of the equation. 17.33333333 + -9.666666667x + -17.33333333 + x2 = 0 + -17.33333333 Reorder the terms: 17.33333333 + -17.33333333 + -9.666666667x + x2 = 0 + -17.33333333 Combine like terms: 17.33333333 + -17.33333333 = 0.00000000 0.00000000 + -9.666666667x + x2 = 0 + -17.33333333 -9.666666667x + x2 = 0 + -17.33333333 Combine like terms: 0 + -17.33333333 = -17.33333333 -9.666666667x + x2 = -17.33333333 The x term is -9.666666667x. Take half its coefficient (-4.833333334). Square it (23.36111112) and add it to both sides. Add '23.36111112' to each side of the equation. -9.666666667x + 23.36111112 + x2 = -17.33333333 + 23.36111112 Reorder the terms: 23.36111112 + -9.666666667x + x2 = -17.33333333 + 23.36111112 Combine like terms: -17.33333333 + 23.36111112 = 6.02777779 23.36111112 + -9.666666667x + x2 = 6.02777779 Factor a perfect square on the left side: (x + -4.833333334)(x + -4.833333334) = 6.02777779 Calculate the square root of the right side: 2.455153313 Break this problem into two subproblems by setting (x + -4.833333334) equal to 2.455153313 and -2.455153313.Subproblem 1
x + -4.833333334 = 2.455153313 Simplifying x + -4.833333334 = 2.455153313 Reorder the terms: -4.833333334 + x = 2.455153313 Solving -4.833333334 + x = 2.455153313 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.833333334' to each side of the equation. -4.833333334 + 4.833333334 + x = 2.455153313 + 4.833333334 Combine like terms: -4.833333334 + 4.833333334 = 0.000000000 0.000000000 + x = 2.455153313 + 4.833333334 x = 2.455153313 + 4.833333334 Combine like terms: 2.455153313 + 4.833333334 = 7.288486647 x = 7.288486647 Simplifying x = 7.288486647Subproblem 2
x + -4.833333334 = -2.455153313 Simplifying x + -4.833333334 = -2.455153313 Reorder the terms: -4.833333334 + x = -2.455153313 Solving -4.833333334 + x = -2.455153313 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.833333334' to each side of the equation. -4.833333334 + 4.833333334 + x = -2.455153313 + 4.833333334 Combine like terms: -4.833333334 + 4.833333334 = 0.000000000 0.000000000 + x = -2.455153313 + 4.833333334 x = -2.455153313 + 4.833333334 Combine like terms: -2.455153313 + 4.833333334 = 2.378180021 x = 2.378180021 Simplifying x = 2.378180021Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.288486647, 2.378180021}Solution
x = {7.288486647, 2.378180021}
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