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Simplifying 62 = 0.5(x2 + -1x) Reorder the terms: 62 = 0.5(-1x + x2) 62 = (-1x * 0.5 + x2 * 0.5) 62 = (-0.5x + 0.5x2) Solving 62 = -0.5x + 0.5x2 Solving for variable 'x'. Reorder the terms: 62 + 0.5x + -0.5x2 = -0.5x + 0.5x + 0.5x2 + -0.5x2 Combine like terms: -0.5x + 0.5x = 0.0 62 + 0.5x + -0.5x2 = 0.0 + 0.5x2 + -0.5x2 62 + 0.5x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 62 + 0.5x + -0.5x2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -124 + -1x + x2 = 0 Move the constant term to the right: Add '124' to each side of the equation. -124 + -1x + 124 + x2 = 0 + 124 Reorder the terms: -124 + 124 + -1x + x2 = 0 + 124 Combine like terms: -124 + 124 = 0 0 + -1x + x2 = 0 + 124 -1x + x2 = 0 + 124 Combine like terms: 0 + 124 = 124 -1x + x2 = 124 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 124 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 124 + 0.25 Combine like terms: 124 + 0.25 = 124.25 0.25 + -1x + x2 = 124.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 124.25 Calculate the square root of the right side: 11.146748405 Break this problem into two subproblems by setting (x + -0.5) equal to 11.146748405 and -11.146748405.Subproblem 1
x + -0.5 = 11.146748405 Simplifying x + -0.5 = 11.146748405 Reorder the terms: -0.5 + x = 11.146748405 Solving -0.5 + x = 11.146748405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 11.146748405 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 11.146748405 + 0.5 x = 11.146748405 + 0.5 Combine like terms: 11.146748405 + 0.5 = 11.646748405 x = 11.646748405 Simplifying x = 11.646748405Subproblem 2
x + -0.5 = -11.146748405 Simplifying x + -0.5 = -11.146748405 Reorder the terms: -0.5 + x = -11.146748405 Solving -0.5 + x = -11.146748405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -11.146748405 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -11.146748405 + 0.5 x = -11.146748405 + 0.5 Combine like terms: -11.146748405 + 0.5 = -10.646748405 x = -10.646748405 Simplifying x = -10.646748405Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.646748405, -10.646748405}
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