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Simplifying 13x2 + -38x + 20 = 0 Reorder the terms: 20 + -38x + 13x2 = 0 Solving 20 + -38x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 1.538461538 + -2.923076923x + x2 = 0 Move the constant term to the right: Add '-1.538461538' to each side of the equation. 1.538461538 + -2.923076923x + -1.538461538 + x2 = 0 + -1.538461538 Reorder the terms: 1.538461538 + -1.538461538 + -2.923076923x + x2 = 0 + -1.538461538 Combine like terms: 1.538461538 + -1.538461538 = 0.000000000 0.000000000 + -2.923076923x + x2 = 0 + -1.538461538 -2.923076923x + x2 = 0 + -1.538461538 Combine like terms: 0 + -1.538461538 = -1.538461538 -2.923076923x + x2 = -1.538461538 The x term is -2.923076923x. Take half its coefficient (-1.461538462). Square it (2.136094676) and add it to both sides. Add '2.136094676' to each side of the equation. -2.923076923x + 2.136094676 + x2 = -1.538461538 + 2.136094676 Reorder the terms: 2.136094676 + -2.923076923x + x2 = -1.538461538 + 2.136094676 Combine like terms: -1.538461538 + 2.136094676 = 0.597633138 2.136094676 + -2.923076923x + x2 = 0.597633138 Factor a perfect square on the left side: (x + -1.461538462)(x + -1.461538462) = 0.597633138 Calculate the square root of the right side: 0.773067357 Break this problem into two subproblems by setting (x + -1.461538462) equal to 0.773067357 and -0.773067357.Subproblem 1
x + -1.461538462 = 0.773067357 Simplifying x + -1.461538462 = 0.773067357 Reorder the terms: -1.461538462 + x = 0.773067357 Solving -1.461538462 + x = 0.773067357 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.461538462' to each side of the equation. -1.461538462 + 1.461538462 + x = 0.773067357 + 1.461538462 Combine like terms: -1.461538462 + 1.461538462 = 0.000000000 0.000000000 + x = 0.773067357 + 1.461538462 x = 0.773067357 + 1.461538462 Combine like terms: 0.773067357 + 1.461538462 = 2.234605819 x = 2.234605819 Simplifying x = 2.234605819Subproblem 2
x + -1.461538462 = -0.773067357 Simplifying x + -1.461538462 = -0.773067357 Reorder the terms: -1.461538462 + x = -0.773067357 Solving -1.461538462 + x = -0.773067357 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.461538462' to each side of the equation. -1.461538462 + 1.461538462 + x = -0.773067357 + 1.461538462 Combine like terms: -1.461538462 + 1.461538462 = 0.000000000 0.000000000 + x = -0.773067357 + 1.461538462 x = -0.773067357 + 1.461538462 Combine like terms: -0.773067357 + 1.461538462 = 0.688471105 x = 0.688471105 Simplifying x = 0.688471105Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.234605819, 0.688471105}
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