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Simplifying x2 = 56 + 23x Solving x2 = 56 + 23x Solving for variable 'x'. Reorder the terms: -56 + -23x + x2 = 56 + 23x + -56 + -23x Reorder the terms: -56 + -23x + x2 = 56 + -56 + 23x + -23x Combine like terms: 56 + -56 = 0 -56 + -23x + x2 = 0 + 23x + -23x -56 + -23x + x2 = 23x + -23x Combine like terms: 23x + -23x = 0 -56 + -23x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + -23x + 56 + x2 = 0 + 56 Reorder the terms: -56 + 56 + -23x + x2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + -23x + x2 = 0 + 56 -23x + x2 = 0 + 56 Combine like terms: 0 + 56 = 56 -23x + x2 = 56 The x term is -23x. Take half its coefficient (-11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. -23x + 132.25 + x2 = 56 + 132.25 Reorder the terms: 132.25 + -23x + x2 = 56 + 132.25 Combine like terms: 56 + 132.25 = 188.25 132.25 + -23x + x2 = 188.25 Factor a perfect square on the left side: (x + -11.5)(x + -11.5) = 188.25 Calculate the square root of the right side: 13.720422734 Break this problem into two subproblems by setting (x + -11.5) equal to 13.720422734 and -13.720422734.Subproblem 1
x + -11.5 = 13.720422734 Simplifying x + -11.5 = 13.720422734 Reorder the terms: -11.5 + x = 13.720422734 Solving -11.5 + x = 13.720422734 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = 13.720422734 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = 13.720422734 + 11.5 x = 13.720422734 + 11.5 Combine like terms: 13.720422734 + 11.5 = 25.220422734 x = 25.220422734 Simplifying x = 25.220422734Subproblem 2
x + -11.5 = -13.720422734 Simplifying x + -11.5 = -13.720422734 Reorder the terms: -11.5 + x = -13.720422734 Solving -11.5 + x = -13.720422734 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = -13.720422734 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = -13.720422734 + 11.5 x = -13.720422734 + 11.5 Combine like terms: -13.720422734 + 11.5 = -2.220422734 x = -2.220422734 Simplifying x = -2.220422734Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.220422734, -2.220422734}
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