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Simplifying x2 + 6x + 8 = 35x2 Reorder the terms: 8 + 6x + x2 = 35x2 Solving 8 + 6x + x2 = 35x2 Solving for variable 'x'. Combine like terms: x2 + -35x2 = -34x2 8 + 6x + -34x2 = 35x2 + -35x2 Combine like terms: 35x2 + -35x2 = 0 8 + 6x + -34x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(4 + 3x + -17x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + 3x + -17x2)' equal to zero and attempt to solve: Simplifying 4 + 3x + -17x2 = 0 Solving 4 + 3x + -17x2 = 0 Begin completing the square. Divide all terms by -17 the coefficient of the squared term: Divide each side by '-17'. -0.2352941176 + -0.1764705882x + x2 = 0 Move the constant term to the right: Add '0.2352941176' to each side of the equation. -0.2352941176 + -0.1764705882x + 0.2352941176 + x2 = 0 + 0.2352941176 Reorder the terms: -0.2352941176 + 0.2352941176 + -0.1764705882x + x2 = 0 + 0.2352941176 Combine like terms: -0.2352941176 + 0.2352941176 = 0.0000000000 0.0000000000 + -0.1764705882x + x2 = 0 + 0.2352941176 -0.1764705882x + x2 = 0 + 0.2352941176 Combine like terms: 0 + 0.2352941176 = 0.2352941176 -0.1764705882x + x2 = 0.2352941176 The x term is -0.1764705882x. Take half its coefficient (-0.0882352941). Square it (0.007785467125) and add it to both sides. Add '0.007785467125' to each side of the equation. -0.1764705882x + 0.007785467125 + x2 = 0.2352941176 + 0.007785467125 Reorder the terms: 0.007785467125 + -0.1764705882x + x2 = 0.2352941176 + 0.007785467125 Combine like terms: 0.2352941176 + 0.007785467125 = 0.243079584725 0.007785467125 + -0.1764705882x + x2 = 0.243079584725 Factor a perfect square on the left side: (x + -0.0882352941)(x + -0.0882352941) = 0.243079584725 Calculate the square root of the right side: 0.493031018 Break this problem into two subproblems by setting (x + -0.0882352941) equal to 0.493031018 and -0.493031018.Subproblem 1
x + -0.0882352941 = 0.493031018 Simplifying x + -0.0882352941 = 0.493031018 Reorder the terms: -0.0882352941 + x = 0.493031018 Solving -0.0882352941 + x = 0.493031018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0882352941' to each side of the equation. -0.0882352941 + 0.0882352941 + x = 0.493031018 + 0.0882352941 Combine like terms: -0.0882352941 + 0.0882352941 = 0.0000000000 0.0000000000 + x = 0.493031018 + 0.0882352941 x = 0.493031018 + 0.0882352941 Combine like terms: 0.493031018 + 0.0882352941 = 0.5812663121 x = 0.5812663121 Simplifying x = 0.5812663121Subproblem 2
x + -0.0882352941 = -0.493031018 Simplifying x + -0.0882352941 = -0.493031018 Reorder the terms: -0.0882352941 + x = -0.493031018 Solving -0.0882352941 + x = -0.493031018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0882352941' to each side of the equation. -0.0882352941 + 0.0882352941 + x = -0.493031018 + 0.0882352941 Combine like terms: -0.0882352941 + 0.0882352941 = 0.0000000000 0.0000000000 + x = -0.493031018 + 0.0882352941 x = -0.493031018 + 0.0882352941 Combine like terms: -0.493031018 + 0.0882352941 = -0.4047957239 x = -0.4047957239 Simplifying x = -0.4047957239Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5812663121, -0.4047957239}Solution
x = {0.5812663121, -0.4047957239}
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