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Simplifying (2x2) + -1x + -59 = 0 Reorder the terms: -59 + -1x + (2x2) = 0 Solving -59 + -1x + (2x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -29.5 + -0.5x + x2 = 0 Move the constant term to the right: Add '29.5' to each side of the equation. -29.5 + -0.5x + 29.5 + x2 = 0 + 29.5 Reorder the terms: -29.5 + 29.5 + -0.5x + x2 = 0 + 29.5 Combine like terms: -29.5 + 29.5 = 0.0 0.0 + -0.5x + x2 = 0 + 29.5 -0.5x + x2 = 0 + 29.5 Combine like terms: 0 + 29.5 = 29.5 -0.5x + x2 = 29.5 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 = 29.5 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 29.5 + 0.0625 Combine like terms: 29.5 + 0.0625 = 29.5625 0.0625 + -0.5x + x2 = 29.5625 Factor a perfect square on the left side: ((x) + -0.25)((x) + -0.25) = 29.5625 Calculate the square root of the right side: 5.437140793 Break this problem into two subproblems by setting ((x) + -0.25) equal to 5.437140793 and -5.437140793.Subproblem 1
(x) + -0.25 = 5.437140793 Simplifying (x) + -0.25 = 5.437140793 x + -0.25 = 5.437140793 Reorder the terms: -0.25 + x = 5.437140793 Solving -0.25 + x = 5.437140793 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 = 5.437140793 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 5.437140793 + 0.25 x = 5.437140793 + 0.25 Combine like terms: 5.437140793 + 0.25 = 5.687140793 x = 5.687140793 Simplifying x = 5.687140793Subproblem 2
(x) + -0.25 = -5.437140793 Simplifying (x) + -0.25 = -5.437140793 x + -0.25 = -5.437140793 Reorder the terms: -0.25 + x = -5.437140793 Solving -0.25 + x = -5.437140793 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 = -5.437140793 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -5.437140793 + 0.25 x = -5.437140793 + 0.25 Combine like terms: -5.437140793 + 0.25 = -5.187140793 x = -5.187140793 Simplifying x = -5.187140793Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.687140793, -5.187140793}
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