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Simplifying 35x2 + 6x + -36 = 0 Reorder the terms: -36 + 6x + 35x2 = 0 Solving -36 + 6x + 35x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -1.028571429 + 0.1714285714x + x2 = 0 Move the constant term to the right: Add '1.028571429' to each side of the equation. -1.028571429 + 0.1714285714x + 1.028571429 + x2 = 0 + 1.028571429 Reorder the terms: -1.028571429 + 1.028571429 + 0.1714285714x + x2 = 0 + 1.028571429 Combine like terms: -1.028571429 + 1.028571429 = 0.000000000 0.000000000 + 0.1714285714x + x2 = 0 + 1.028571429 0.1714285714x + x2 = 0 + 1.028571429 Combine like terms: 0 + 1.028571429 = 1.028571429 0.1714285714x + x2 = 1.028571429 The x term is 0.1714285714x. Take half its coefficient (0.0857142857). Square it (0.007346938773) and add it to both sides. Add '0.007346938773' to each side of the equation. 0.1714285714x + 0.007346938773 + x2 = 1.028571429 + 0.007346938773 Reorder the terms: 0.007346938773 + 0.1714285714x + x2 = 1.028571429 + 0.007346938773 Combine like terms: 1.028571429 + 0.007346938773 = 1.035918367773 0.007346938773 + 0.1714285714x + x2 = 1.035918367773 Factor a perfect square on the left side: (x + 0.0857142857)(x + 0.0857142857) = 1.035918367773 Calculate the square root of the right side: 1.017800751 Break this problem into two subproblems by setting (x + 0.0857142857) equal to 1.017800751 and -1.017800751.Subproblem 1
x + 0.0857142857 = 1.017800751 Simplifying x + 0.0857142857 = 1.017800751 Reorder the terms: 0.0857142857 + x = 1.017800751 Solving 0.0857142857 + x = 1.017800751 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0857142857' to each side of the equation. 0.0857142857 + -0.0857142857 + x = 1.017800751 + -0.0857142857 Combine like terms: 0.0857142857 + -0.0857142857 = 0.0000000000 0.0000000000 + x = 1.017800751 + -0.0857142857 x = 1.017800751 + -0.0857142857 Combine like terms: 1.017800751 + -0.0857142857 = 0.9320864653 x = 0.9320864653 Simplifying x = 0.9320864653Subproblem 2
x + 0.0857142857 = -1.017800751 Simplifying x + 0.0857142857 = -1.017800751 Reorder the terms: 0.0857142857 + x = -1.017800751 Solving 0.0857142857 + x = -1.017800751 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0857142857' to each side of the equation. 0.0857142857 + -0.0857142857 + x = -1.017800751 + -0.0857142857 Combine like terms: 0.0857142857 + -0.0857142857 = 0.0000000000 0.0000000000 + x = -1.017800751 + -0.0857142857 x = -1.017800751 + -0.0857142857 Combine like terms: -1.017800751 + -0.0857142857 = -1.1035150367 x = -1.1035150367 Simplifying x = -1.1035150367Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9320864653, -1.1035150367}
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