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Simplifying -1x2 + 59 = x Reorder the terms: 59 + -1x2 = x Solving 59 + -1x2 = x Solving for variable 'x'. Reorder the terms: 59 + -1x + -1x2 = x + -1x Combine like terms: x + -1x = 0 59 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -59 + x + x2 = 0 Move the constant term to the right: Add '59' to each side of the equation. -59 + x + 59 + x2 = 0 + 59 Reorder the terms: -59 + 59 + x + x2 = 0 + 59 Combine like terms: -59 + 59 = 0 0 + x + x2 = 0 + 59 x + x2 = 0 + 59 Combine like terms: 0 + 59 = 59 x + x2 = 59 The x term is x. 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. + 0.25 + x2 = 59 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 59 + 0.25 Combine like terms: 59 + 0.25 = 59.25 1.25 + x2 = 59.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 59.25 Calculate the square root of the right side: 7.697402159 Break this problem into two subproblems by setting (x + 0.5) equal to 7.697402159 and -7.697402159.Subproblem 1
x + 0.5 = 7.697402159 Simplifying x + 0.5 = 7.697402159 Reorder the terms: 0.5 + x = 7.697402159 Solving 0.5 + x = 7.697402159 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 = 7.697402159 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 7.697402159 + -0.5 x = 7.697402159 + -0.5 Combine like terms: 7.697402159 + -0.5 = 7.197402159 x = 7.197402159 Simplifying x = 7.197402159Subproblem 2
x + 0.5 = -7.697402159 Simplifying x + 0.5 = -7.697402159 Reorder the terms: 0.5 + x = -7.697402159 Solving 0.5 + x = -7.697402159 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 = -7.697402159 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -7.697402159 + -0.5 x = -7.697402159 + -0.5 Combine like terms: -7.697402159 + -0.5 = -8.197402159 x = -8.197402159 Simplifying x = -8.197402159Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.197402159, -8.197402159}
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