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Simplifying 2x(-13x + 22) = 16 Reorder the terms: 2x(22 + -13x) = 16 (22 * 2x + -13x * 2x) = 16 (44x + -26x2) = 16 Solving 44x + -26x2 = 16 Solving for variable 'x'. Reorder the terms: -16 + 44x + -26x2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + 44x + -26x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + 22x + -13x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + 22x + -13x2)' equal to zero and attempt to solve: Simplifying -8 + 22x + -13x2 = 0 Solving -8 + 22x + -13x2 = 0 Begin completing the square. Divide all terms by -13 the coefficient of the squared term: Divide each side by '-13'. 0.6153846154 + -1.692307692x + x2 = 0 Move the constant term to the right: Add '-0.6153846154' to each side of the equation. 0.6153846154 + -1.692307692x + -0.6153846154 + x2 = 0 + -0.6153846154 Reorder the terms: 0.6153846154 + -0.6153846154 + -1.692307692x + x2 = 0 + -0.6153846154 Combine like terms: 0.6153846154 + -0.6153846154 = 0.0000000000 0.0000000000 + -1.692307692x + x2 = 0 + -0.6153846154 -1.692307692x + x2 = 0 + -0.6153846154 Combine like terms: 0 + -0.6153846154 = -0.6153846154 -1.692307692x + x2 = -0.6153846154 The x term is -1.692307692x. Take half its coefficient (-0.846153846). Square it (0.7159763311) and add it to both sides. Add '0.7159763311' to each side of the equation. -1.692307692x + 0.7159763311 + x2 = -0.6153846154 + 0.7159763311 Reorder the terms: 0.7159763311 + -1.692307692x + x2 = -0.6153846154 + 0.7159763311 Combine like terms: -0.6153846154 + 0.7159763311 = 0.1005917157 0.7159763311 + -1.692307692x + x2 = 0.1005917157 Factor a perfect square on the left side: (x + -0.846153846)(x + -0.846153846) = 0.1005917157 Calculate the square root of the right side: 0.317161971 Break this problem into two subproblems by setting (x + -0.846153846) equal to 0.317161971 and -0.317161971.Subproblem 1
x + -0.846153846 = 0.317161971 Simplifying x + -0.846153846 = 0.317161971 Reorder the terms: -0.846153846 + x = 0.317161971 Solving -0.846153846 + x = 0.317161971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.846153846' to each side of the equation. -0.846153846 + 0.846153846 + x = 0.317161971 + 0.846153846 Combine like terms: -0.846153846 + 0.846153846 = 0.000000000 0.000000000 + x = 0.317161971 + 0.846153846 x = 0.317161971 + 0.846153846 Combine like terms: 0.317161971 + 0.846153846 = 1.163315817 x = 1.163315817 Simplifying x = 1.163315817Subproblem 2
x + -0.846153846 = -0.317161971 Simplifying x + -0.846153846 = -0.317161971 Reorder the terms: -0.846153846 + x = -0.317161971 Solving -0.846153846 + x = -0.317161971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.846153846' to each side of the equation. -0.846153846 + 0.846153846 + x = -0.317161971 + 0.846153846 Combine like terms: -0.846153846 + 0.846153846 = 0.000000000 0.000000000 + x = -0.317161971 + 0.846153846 x = -0.317161971 + 0.846153846 Combine like terms: -0.317161971 + 0.846153846 = 0.528991875 x = 0.528991875 Simplifying x = 0.528991875Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.163315817, 0.528991875}Solution
x = {1.163315817, 0.528991875}
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