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Simplifying 35x2 + -6x + -37 = 0 Reorder the terms: -37 + -6x + 35x2 = 0 Solving -37 + -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'. -1.057142857 + -0.1714285714x + x2 = 0 Move the constant term to the right: Add '1.057142857' to each side of the equation. -1.057142857 + -0.1714285714x + 1.057142857 + x2 = 0 + 1.057142857 Reorder the terms: -1.057142857 + 1.057142857 + -0.1714285714x + x2 = 0 + 1.057142857 Combine like terms: -1.057142857 + 1.057142857 = 0.000000000 0.000000000 + -0.1714285714x + x2 = 0 + 1.057142857 -0.1714285714x + x2 = 0 + 1.057142857 Combine like terms: 0 + 1.057142857 = 1.057142857 -0.1714285714x + x2 = 1.057142857 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 = 1.057142857 + 0.007346938773 Reorder the terms: 0.007346938773 + -0.1714285714x + x2 = 1.057142857 + 0.007346938773 Combine like terms: 1.057142857 + 0.007346938773 = 1.064489795773 0.007346938773 + -0.1714285714x + x2 = 1.064489795773 Factor a perfect square on the left side: (x + -0.0857142857)(x + -0.0857142857) = 1.064489795773 Calculate the square root of the right side: 1.031741148 Break this problem into two subproblems by setting (x + -0.0857142857) equal to 1.031741148 and -1.031741148.Subproblem 1
x + -0.0857142857 = 1.031741148 Simplifying x + -0.0857142857 = 1.031741148 Reorder the terms: -0.0857142857 + x = 1.031741148 Solving -0.0857142857 + x = 1.031741148 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 = 1.031741148 + 0.0857142857 Combine like terms: -0.0857142857 + 0.0857142857 = 0.0000000000 0.0000000000 + x = 1.031741148 + 0.0857142857 x = 1.031741148 + 0.0857142857 Combine like terms: 1.031741148 + 0.0857142857 = 1.1174554337 x = 1.1174554337 Simplifying x = 1.1174554337Subproblem 2
x + -0.0857142857 = -1.031741148 Simplifying x + -0.0857142857 = -1.031741148 Reorder the terms: -0.0857142857 + x = -1.031741148 Solving -0.0857142857 + x = -1.031741148 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 = -1.031741148 + 0.0857142857 Combine like terms: -0.0857142857 + 0.0857142857 = 0.0000000000 0.0000000000 + x = -1.031741148 + 0.0857142857 x = -1.031741148 + 0.0857142857 Combine like terms: -1.031741148 + 0.0857142857 = -0.9460268623 x = -0.9460268623 Simplifying x = -0.9460268623Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1174554337, -0.9460268623}
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