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Simplifying 13x2 + 5x + -8 = 6 + x Reorder the terms: -8 + 5x + 13x2 = 6 + x Solving -8 + 5x + 13x2 = 6 + x Solving for variable 'x'. Reorder the terms: -8 + -6 + 5x + -1x + 13x2 = 6 + x + -6 + -1x Combine like terms: -8 + -6 = -14 -14 + 5x + -1x + 13x2 = 6 + x + -6 + -1x Combine like terms: 5x + -1x = 4x -14 + 4x + 13x2 = 6 + x + -6 + -1x Reorder the terms: -14 + 4x + 13x2 = 6 + -6 + x + -1x Combine like terms: 6 + -6 = 0 -14 + 4x + 13x2 = 0 + x + -1x -14 + 4x + 13x2 = x + -1x Combine like terms: x + -1x = 0 -14 + 4x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -1.076923077 + 0.3076923077x + x2 = 0 Move the constant term to the right: Add '1.076923077' to each side of the equation. -1.076923077 + 0.3076923077x + 1.076923077 + x2 = 0 + 1.076923077 Reorder the terms: -1.076923077 + 1.076923077 + 0.3076923077x + x2 = 0 + 1.076923077 Combine like terms: -1.076923077 + 1.076923077 = 0.000000000 0.000000000 + 0.3076923077x + x2 = 0 + 1.076923077 0.3076923077x + x2 = 0 + 1.076923077 Combine like terms: 0 + 1.076923077 = 1.076923077 0.3076923077x + x2 = 1.076923077 The x term is 0.3076923077x. Take half its coefficient (0.1538461539). Square it (0.02366863907) and add it to both sides. Add '0.02366863907' to each side of the equation. 0.3076923077x + 0.02366863907 + x2 = 1.076923077 + 0.02366863907 Reorder the terms: 0.02366863907 + 0.3076923077x + x2 = 1.076923077 + 0.02366863907 Combine like terms: 1.076923077 + 0.02366863907 = 1.10059171607 0.02366863907 + 0.3076923077x + x2 = 1.10059171607 Factor a perfect square on the left side: (x + 0.1538461539)(x + 0.1538461539) = 1.10059171607 Calculate the square root of the right side: 1.0490909 Break this problem into two subproblems by setting (x + 0.1538461539) equal to 1.0490909 and -1.0490909.Subproblem 1
x + 0.1538461539 = 1.0490909 Simplifying x + 0.1538461539 = 1.0490909 Reorder the terms: 0.1538461539 + x = 1.0490909 Solving 0.1538461539 + x = 1.0490909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1538461539' to each side of the equation. 0.1538461539 + -0.1538461539 + x = 1.0490909 + -0.1538461539 Combine like terms: 0.1538461539 + -0.1538461539 = 0.0000000000 0.0000000000 + x = 1.0490909 + -0.1538461539 x = 1.0490909 + -0.1538461539 Combine like terms: 1.0490909 + -0.1538461539 = 0.8952447461 x = 0.8952447461 Simplifying x = 0.8952447461Subproblem 2
x + 0.1538461539 = -1.0490909 Simplifying x + 0.1538461539 = -1.0490909 Reorder the terms: 0.1538461539 + x = -1.0490909 Solving 0.1538461539 + x = -1.0490909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1538461539' to each side of the equation. 0.1538461539 + -0.1538461539 + x = -1.0490909 + -0.1538461539 Combine like terms: 0.1538461539 + -0.1538461539 = 0.0000000000 0.0000000000 + x = -1.0490909 + -0.1538461539 x = -1.0490909 + -0.1538461539 Combine like terms: -1.0490909 + -0.1538461539 = -1.2029370539 x = -1.2029370539 Simplifying x = -1.2029370539Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8952447461, -1.2029370539}
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