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Simplifying 5x + 44 = x2 + -2 Reorder the terms: 44 + 5x = x2 + -2 Reorder the terms: 44 + 5x = -2 + x2 Solving 44 + 5x = -2 + x2 Solving for variable 'x'. Reorder the terms: 44 + 2 + 5x + -1x2 = -2 + x2 + 2 + -1x2 Combine like terms: 44 + 2 = 46 46 + 5x + -1x2 = -2 + x2 + 2 + -1x2 Reorder the terms: 46 + 5x + -1x2 = -2 + 2 + x2 + -1x2 Combine like terms: -2 + 2 = 0 46 + 5x + -1x2 = 0 + x2 + -1x2 46 + 5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 46 + 5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -46 + -5x + x2 = 0 Move the constant term to the right: Add '46' to each side of the equation. -46 + -5x + 46 + x2 = 0 + 46 Reorder the terms: -46 + 46 + -5x + x2 = 0 + 46 Combine like terms: -46 + 46 = 0 0 + -5x + x2 = 0 + 46 -5x + x2 = 0 + 46 Combine like terms: 0 + 46 = 46 -5x + x2 = 46 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 46 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 46 + 6.25 Combine like terms: 46 + 6.25 = 52.25 6.25 + -5x + x2 = 52.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 52.25 Calculate the square root of the right side: 7.228416147 Break this problem into two subproblems by setting (x + -2.5) equal to 7.228416147 and -7.228416147.Subproblem 1
x + -2.5 = 7.228416147 Simplifying x + -2.5 = 7.228416147 Reorder the terms: -2.5 + x = 7.228416147 Solving -2.5 + x = 7.228416147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 7.228416147 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 7.228416147 + 2.5 x = 7.228416147 + 2.5 Combine like terms: 7.228416147 + 2.5 = 9.728416147 x = 9.728416147 Simplifying x = 9.728416147Subproblem 2
x + -2.5 = -7.228416147 Simplifying x + -2.5 = -7.228416147 Reorder the terms: -2.5 + x = -7.228416147 Solving -2.5 + x = -7.228416147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -7.228416147 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -7.228416147 + 2.5 x = -7.228416147 + 2.5 Combine like terms: -7.228416147 + 2.5 = -4.728416147 x = -4.728416147 Simplifying x = -4.728416147Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.728416147, -4.728416147}
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