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Simplifying 13x2 + -14x + 2 = 0 Reorder the terms: 2 + -14x + 13x2 = 0 Solving 2 + -14x + 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'. 0.1538461538 + -1.076923077x + x2 = 0 Move the constant term to the right: Add '-0.1538461538' to each side of the equation. 0.1538461538 + -1.076923077x + -0.1538461538 + x2 = 0 + -0.1538461538 Reorder the terms: 0.1538461538 + -0.1538461538 + -1.076923077x + x2 = 0 + -0.1538461538 Combine like terms: 0.1538461538 + -0.1538461538 = 0.0000000000 0.0000000000 + -1.076923077x + x2 = 0 + -0.1538461538 -1.076923077x + x2 = 0 + -0.1538461538 Combine like terms: 0 + -0.1538461538 = -0.1538461538 -1.076923077x + x2 = -0.1538461538 The x term is -1.076923077x. Take half its coefficient (-0.5384615385). Square it (0.2899408284) and add it to both sides. Add '0.2899408284' to each side of the equation. -1.076923077x + 0.2899408284 + x2 = -0.1538461538 + 0.2899408284 Reorder the terms: 0.2899408284 + -1.076923077x + x2 = -0.1538461538 + 0.2899408284 Combine like terms: -0.1538461538 + 0.2899408284 = 0.1360946746 0.2899408284 + -1.076923077x + x2 = 0.1360946746 Factor a perfect square on the left side: (x + -0.5384615385)(x + -0.5384615385) = 0.1360946746 Calculate the square root of the right side: 0.368910117 Break this problem into two subproblems by setting (x + -0.5384615385) equal to 0.368910117 and -0.368910117.Subproblem 1
x + -0.5384615385 = 0.368910117 Simplifying x + -0.5384615385 = 0.368910117 Reorder the terms: -0.5384615385 + x = 0.368910117 Solving -0.5384615385 + x = 0.368910117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5384615385' to each side of the equation. -0.5384615385 + 0.5384615385 + x = 0.368910117 + 0.5384615385 Combine like terms: -0.5384615385 + 0.5384615385 = 0.0000000000 0.0000000000 + x = 0.368910117 + 0.5384615385 x = 0.368910117 + 0.5384615385 Combine like terms: 0.368910117 + 0.5384615385 = 0.9073716555 x = 0.9073716555 Simplifying x = 0.9073716555Subproblem 2
x + -0.5384615385 = -0.368910117 Simplifying x + -0.5384615385 = -0.368910117 Reorder the terms: -0.5384615385 + x = -0.368910117 Solving -0.5384615385 + x = -0.368910117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5384615385' to each side of the equation. -0.5384615385 + 0.5384615385 + x = -0.368910117 + 0.5384615385 Combine like terms: -0.5384615385 + 0.5384615385 = 0.0000000000 0.0000000000 + x = -0.368910117 + 0.5384615385 x = -0.368910117 + 0.5384615385 Combine like terms: -0.368910117 + 0.5384615385 = 0.1695514215 x = 0.1695514215 Simplifying x = 0.1695514215Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9073716555, 0.1695514215}
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