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Simplifying x2 + -2x + -24 = 3 + -1x + 4 Reorder the terms: -24 + -2x + x2 = 3 + -1x + 4 Reorder the terms: -24 + -2x + x2 = 3 + 4 + -1x Combine like terms: 3 + 4 = 7 -24 + -2x + x2 = 7 + -1x Solving -24 + -2x + x2 = 7 + -1x Solving for variable 'x'. Reorder the terms: -24 + -7 + -2x + x + x2 = 7 + -1x + -7 + x Combine like terms: -24 + -7 = -31 -31 + -2x + x + x2 = 7 + -1x + -7 + x Combine like terms: -2x + x = -1x -31 + -1x + x2 = 7 + -1x + -7 + x Reorder the terms: -31 + -1x + x2 = 7 + -7 + -1x + x Combine like terms: 7 + -7 = 0 -31 + -1x + x2 = 0 + -1x + x -31 + -1x + x2 = -1x + x Combine like terms: -1x + x = 0 -31 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '31' to each side of the equation. -31 + -1x + 31 + x2 = 0 + 31 Reorder the terms: -31 + 31 + -1x + x2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + -1x + x2 = 0 + 31 -1x + x2 = 0 + 31 Combine like terms: 0 + 31 = 31 -1x + x2 = 31 The x term is -1x. 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. -1x + 0.25 + x2 = 31 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 31 + 0.25 Combine like terms: 31 + 0.25 = 31.25 0.25 + -1x + x2 = 31.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 31.25 Calculate the square root of the right side: 5.590169944 Break this problem into two subproblems by setting (x + -0.5) equal to 5.590169944 and -5.590169944.Subproblem 1
x + -0.5 = 5.590169944 Simplifying x + -0.5 = 5.590169944 Reorder the terms: -0.5 + x = 5.590169944 Solving -0.5 + x = 5.590169944 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 = 5.590169944 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 5.590169944 + 0.5 x = 5.590169944 + 0.5 Combine like terms: 5.590169944 + 0.5 = 6.090169944 x = 6.090169944 Simplifying x = 6.090169944Subproblem 2
x + -0.5 = -5.590169944 Simplifying x + -0.5 = -5.590169944 Reorder the terms: -0.5 + x = -5.590169944 Solving -0.5 + x = -5.590169944 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 = -5.590169944 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -5.590169944 + 0.5 x = -5.590169944 + 0.5 Combine like terms: -5.590169944 + 0.5 = -5.090169944 x = -5.090169944 Simplifying x = -5.090169944Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.090169944, -5.090169944}
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