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Simplifying 14x2 + -82x + 10 = 0 Reorder the terms: 10 + -82x + 14x2 = 0 Solving 10 + -82x + 14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -41x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -41x + 7x2)' equal to zero and attempt to solve: Simplifying 5 + -41x + 7x2 = 0 Solving 5 + -41x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.7142857143 + -5.857142857x + x2 = 0 Move the constant term to the right: Add '-0.7142857143' to each side of the equation. 0.7142857143 + -5.857142857x + -0.7142857143 + x2 = 0 + -0.7142857143 Reorder the terms: 0.7142857143 + -0.7142857143 + -5.857142857x + x2 = 0 + -0.7142857143 Combine like terms: 0.7142857143 + -0.7142857143 = 0.0000000000 0.0000000000 + -5.857142857x + x2 = 0 + -0.7142857143 -5.857142857x + x2 = 0 + -0.7142857143 Combine like terms: 0 + -0.7142857143 = -0.7142857143 -5.857142857x + x2 = -0.7142857143 The x term is -5.857142857x. Take half its coefficient (-2.928571429). Square it (8.576530615) and add it to both sides. Add '8.576530615' to each side of the equation. -5.857142857x + 8.576530615 + x2 = -0.7142857143 + 8.576530615 Reorder the terms: 8.576530615 + -5.857142857x + x2 = -0.7142857143 + 8.576530615 Combine like terms: -0.7142857143 + 8.576530615 = 7.8622449007 8.576530615 + -5.857142857x + x2 = 7.8622449007 Factor a perfect square on the left side: (x + -2.928571429)(x + -2.928571429) = 7.8622449007 Calculate the square root of the right side: 2.80396949 Break this problem into two subproblems by setting (x + -2.928571429) equal to 2.80396949 and -2.80396949.Subproblem 1
x + -2.928571429 = 2.80396949 Simplifying x + -2.928571429 = 2.80396949 Reorder the terms: -2.928571429 + x = 2.80396949 Solving -2.928571429 + x = 2.80396949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.928571429' to each side of the equation. -2.928571429 + 2.928571429 + x = 2.80396949 + 2.928571429 Combine like terms: -2.928571429 + 2.928571429 = 0.000000000 0.000000000 + x = 2.80396949 + 2.928571429 x = 2.80396949 + 2.928571429 Combine like terms: 2.80396949 + 2.928571429 = 5.732540919 x = 5.732540919 Simplifying x = 5.732540919Subproblem 2
x + -2.928571429 = -2.80396949 Simplifying x + -2.928571429 = -2.80396949 Reorder the terms: -2.928571429 + x = -2.80396949 Solving -2.928571429 + x = -2.80396949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.928571429' to each side of the equation. -2.928571429 + 2.928571429 + x = -2.80396949 + 2.928571429 Combine like terms: -2.928571429 + 2.928571429 = 0.000000000 0.000000000 + x = -2.80396949 + 2.928571429 x = -2.80396949 + 2.928571429 Combine like terms: -2.80396949 + 2.928571429 = 0.124601939 x = 0.124601939 Simplifying x = 0.124601939Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.732540919, 0.124601939}Solution
x = {5.732540919, 0.124601939}
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