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Simplifying 0 = x2 + -2x + -46 Reorder the terms: 0 = -46 + -2x + x2 Solving 0 = -46 + -2x + x2 Solving for variable 'x'. Combine like terms: 0 + 46 = 46 46 + 2x + -1x2 = -46 + -2x + x2 + 46 + 2x + -1x2 Reorder the terms: 46 + 2x + -1x2 = -46 + 46 + -2x + 2x + x2 + -1x2 Combine like terms: -46 + 46 = 0 46 + 2x + -1x2 = 0 + -2x + 2x + x2 + -1x2 46 + 2x + -1x2 = -2x + 2x + x2 + -1x2 Combine like terms: -2x + 2x = 0 46 + 2x + -1x2 = 0 + x2 + -1x2 46 + 2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 46 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -46 + -2x + x2 = 0 Move the constant term to the right: Add '46' to each side of the equation. -46 + -2x + 46 + x2 = 0 + 46 Reorder the terms: -46 + 46 + -2x + x2 = 0 + 46 Combine like terms: -46 + 46 = 0 0 + -2x + x2 = 0 + 46 -2x + x2 = 0 + 46 Combine like terms: 0 + 46 = 46 -2x + x2 = 46 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 46 + 1 Reorder the terms: 1 + -2x + x2 = 46 + 1 Combine like terms: 46 + 1 = 47 1 + -2x + x2 = 47 Factor a perfect square on the left side: (x + -1)(x + -1) = 47 Calculate the square root of the right side: 6.8556546 Break this problem into two subproblems by setting (x + -1) equal to 6.8556546 and -6.8556546.Subproblem 1
x + -1 = 6.8556546 Simplifying x + -1 = 6.8556546 Reorder the terms: -1 + x = 6.8556546 Solving -1 + x = 6.8556546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 6.8556546 + 1 Combine like terms: -1 + 1 = 0 0 + x = 6.8556546 + 1 x = 6.8556546 + 1 Combine like terms: 6.8556546 + 1 = 7.8556546 x = 7.8556546 Simplifying x = 7.8556546Subproblem 2
x + -1 = -6.8556546 Simplifying x + -1 = -6.8556546 Reorder the terms: -1 + x = -6.8556546 Solving -1 + x = -6.8556546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -6.8556546 + 1 Combine like terms: -1 + 1 = 0 0 + x = -6.8556546 + 1 x = -6.8556546 + 1 Combine like terms: -6.8556546 + 1 = -5.8556546 x = -5.8556546 Simplifying x = -5.8556546Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.8556546, -5.8556546}
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