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Simplifying 13x2 = 24x + -10 Reorder the terms: 13x2 = -10 + 24x Solving 13x2 = -10 + 24x Solving for variable 'x'. Reorder the terms: 10 + -24x + 13x2 = -10 + 24x + 10 + -24x Reorder the terms: 10 + -24x + 13x2 = -10 + 10 + 24x + -24x Combine like terms: -10 + 10 = 0 10 + -24x + 13x2 = 0 + 24x + -24x 10 + -24x + 13x2 = 24x + -24x Combine like terms: 24x + -24x = 0 10 + -24x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 0.7692307692 + -1.846153846x + x2 = 0 Move the constant term to the right: Add '-0.7692307692' to each side of the equation. 0.7692307692 + -1.846153846x + -0.7692307692 + x2 = 0 + -0.7692307692 Reorder the terms: 0.7692307692 + -0.7692307692 + -1.846153846x + x2 = 0 + -0.7692307692 Combine like terms: 0.7692307692 + -0.7692307692 = 0.0000000000 0.0000000000 + -1.846153846x + x2 = 0 + -0.7692307692 -1.846153846x + x2 = 0 + -0.7692307692 Combine like terms: 0 + -0.7692307692 = -0.7692307692 -1.846153846x + x2 = -0.7692307692 The x term is -1.846153846x. Take half its coefficient (-0.923076923). Square it (0.8520710058) and add it to both sides. Add '0.8520710058' to each side of the equation. -1.846153846x + 0.8520710058 + x2 = -0.7692307692 + 0.8520710058 Reorder the terms: 0.8520710058 + -1.846153846x + x2 = -0.7692307692 + 0.8520710058 Combine like terms: -0.7692307692 + 0.8520710058 = 0.0828402366 0.8520710058 + -1.846153846x + x2 = 0.0828402366 Factor a perfect square on the left side: (x + -0.923076923)(x + -0.923076923) = 0.0828402366 Calculate the square root of the right side: 0.287819799 Break this problem into two subproblems by setting (x + -0.923076923) equal to 0.287819799 and -0.287819799.Subproblem 1
x + -0.923076923 = 0.287819799 Simplifying x + -0.923076923 = 0.287819799 Reorder the terms: -0.923076923 + x = 0.287819799 Solving -0.923076923 + x = 0.287819799 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.923076923' to each side of the equation. -0.923076923 + 0.923076923 + x = 0.287819799 + 0.923076923 Combine like terms: -0.923076923 + 0.923076923 = 0.000000000 0.000000000 + x = 0.287819799 + 0.923076923 x = 0.287819799 + 0.923076923 Combine like terms: 0.287819799 + 0.923076923 = 1.210896722 x = 1.210896722 Simplifying x = 1.210896722Subproblem 2
x + -0.923076923 = -0.287819799 Simplifying x + -0.923076923 = -0.287819799 Reorder the terms: -0.923076923 + x = -0.287819799 Solving -0.923076923 + x = -0.287819799 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.923076923' to each side of the equation. -0.923076923 + 0.923076923 + x = -0.287819799 + 0.923076923 Combine like terms: -0.923076923 + 0.923076923 = 0.000000000 0.000000000 + x = -0.287819799 + 0.923076923 x = -0.287819799 + 0.923076923 Combine like terms: -0.287819799 + 0.923076923 = 0.635257124 x = 0.635257124 Simplifying x = 0.635257124Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.210896722, 0.635257124}
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