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Simplifying -1x2 + 3 = (2x + -1) * 62 Reorder the terms: 3 + -1x2 = (2x + -1) * 62 Reorder the terms: 3 + -1x2 = (-1 + 2x) * 62 Reorder the terms for easier multiplication: 3 + -1x2 = 62(-1 + 2x) 3 + -1x2 = (-1 * 62 + 2x * 62) 3 + -1x2 = (-62 + 124x) Solving 3 + -1x2 = -62 + 124x Solving for variable 'x'. Reorder the terms: 3 + 62 + -124x + -1x2 = -62 + 124x + 62 + -124x Combine like terms: 3 + 62 = 65 65 + -124x + -1x2 = -62 + 124x + 62 + -124x Reorder the terms: 65 + -124x + -1x2 = -62 + 62 + 124x + -124x Combine like terms: -62 + 62 = 0 65 + -124x + -1x2 = 0 + 124x + -124x 65 + -124x + -1x2 = 124x + -124x Combine like terms: 124x + -124x = 0 65 + -124x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -65 + 124x + x2 = 0 Move the constant term to the right: Add '65' to each side of the equation. -65 + 124x + 65 + x2 = 0 + 65 Reorder the terms: -65 + 65 + 124x + x2 = 0 + 65 Combine like terms: -65 + 65 = 0 0 + 124x + x2 = 0 + 65 124x + x2 = 0 + 65 Combine like terms: 0 + 65 = 65 124x + x2 = 65 The x term is 124x. Take half its coefficient (62). Square it (3844) and add it to both sides. Add '3844' to each side of the equation. 124x + 3844 + x2 = 65 + 3844 Reorder the terms: 3844 + 124x + x2 = 65 + 3844 Combine like terms: 65 + 3844 = 3909 3844 + 124x + x2 = 3909 Factor a perfect square on the left side: (x + 62)(x + 62) = 3909 Calculate the square root of the right side: 62.521996129 Break this problem into two subproblems by setting (x + 62) equal to 62.521996129 and -62.521996129.Subproblem 1
x + 62 = 62.521996129 Simplifying x + 62 = 62.521996129 Reorder the terms: 62 + x = 62.521996129 Solving 62 + x = 62.521996129 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-62' to each side of the equation. 62 + -62 + x = 62.521996129 + -62 Combine like terms: 62 + -62 = 0 0 + x = 62.521996129 + -62 x = 62.521996129 + -62 Combine like terms: 62.521996129 + -62 = 0.521996129 x = 0.521996129 Simplifying x = 0.521996129Subproblem 2
x + 62 = -62.521996129 Simplifying x + 62 = -62.521996129 Reorder the terms: 62 + x = -62.521996129 Solving 62 + x = -62.521996129 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-62' to each side of the equation. 62 + -62 + x = -62.521996129 + -62 Combine like terms: 62 + -62 = 0 0 + x = -62.521996129 + -62 x = -62.521996129 + -62 Combine like terms: -62.521996129 + -62 = -124.521996129 x = -124.521996129 Simplifying x = -124.521996129Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.521996129, -124.521996129}
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