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Simplifying x(2x + -1) = 58 Reorder the terms: x(-1 + 2x) = 58 (-1 * x + 2x * x) = 58 (-1x + 2x2) = 58 Solving -1x + 2x2 = 58 Solving for variable 'x'. Reorder the terms: -58 + -1x + 2x2 = 58 + -58 Combine like terms: 58 + -58 = 0 -58 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -29 + -0.5x + x2 = 0 Move the constant term to the right: Add '29' to each side of the equation. -29 + -0.5x + 29 + x2 = 0 + 29 Reorder the terms: -29 + 29 + -0.5x + x2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + -0.5x + x2 = 0 + 29 -0.5x + x2 = 0 + 29 Combine like terms: 0 + 29 = 29 -0.5x + x2 = 29 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 29 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 29 + 0.0625 Combine like terms: 29 + 0.0625 = 29.0625 0.0625 + -0.5x + x2 = 29.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 29.0625 Calculate the square root of the right side: 5.390964663 Break this problem into two subproblems by setting (x + -0.25) equal to 5.390964663 and -5.390964663.Subproblem 1
x + -0.25 = 5.390964663 Simplifying x + -0.25 = 5.390964663 Reorder the terms: -0.25 + x = 5.390964663 Solving -0.25 + x = 5.390964663 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 5.390964663 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 5.390964663 + 0.25 x = 5.390964663 + 0.25 Combine like terms: 5.390964663 + 0.25 = 5.640964663 x = 5.640964663 Simplifying x = 5.640964663Subproblem 2
x + -0.25 = -5.390964663 Simplifying x + -0.25 = -5.390964663 Reorder the terms: -0.25 + x = -5.390964663 Solving -0.25 + x = -5.390964663 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -5.390964663 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -5.390964663 + 0.25 x = -5.390964663 + 0.25 Combine like terms: -5.390964663 + 0.25 = -5.140964663 x = -5.140964663 Simplifying x = -5.140964663Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.640964663, -5.140964663}
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