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Simplifying x2 + -2x + -24 = x + -3 Reorder the terms: -24 + -2x + x2 = x + -3 Reorder the terms: -24 + -2x + x2 = -3 + x Solving -24 + -2x + x2 = -3 + x Solving for variable 'x'. Reorder the terms: -24 + 3 + -2x + -1x + x2 = -3 + x + 3 + -1x Combine like terms: -24 + 3 = -21 -21 + -2x + -1x + x2 = -3 + x + 3 + -1x Combine like terms: -2x + -1x = -3x -21 + -3x + x2 = -3 + x + 3 + -1x Reorder the terms: -21 + -3x + x2 = -3 + 3 + x + -1x Combine like terms: -3 + 3 = 0 -21 + -3x + x2 = 0 + x + -1x -21 + -3x + x2 = x + -1x Combine like terms: x + -1x = 0 -21 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + -3x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + -3x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -3x + x2 = 0 + 21 -3x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 -3x + x2 = 21 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 21 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 21 + 2.25 Combine like terms: 21 + 2.25 = 23.25 2.25 + -3x + x2 = 23.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 23.25 Calculate the square root of the right side: 4.82182538 Break this problem into two subproblems by setting (x + -1.5) equal to 4.82182538 and -4.82182538.Subproblem 1
x + -1.5 = 4.82182538 Simplifying x + -1.5 = 4.82182538 Reorder the terms: -1.5 + x = 4.82182538 Solving -1.5 + x = 4.82182538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 4.82182538 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 4.82182538 + 1.5 x = 4.82182538 + 1.5 Combine like terms: 4.82182538 + 1.5 = 6.32182538 x = 6.32182538 Simplifying x = 6.32182538Subproblem 2
x + -1.5 = -4.82182538 Simplifying x + -1.5 = -4.82182538 Reorder the terms: -1.5 + x = -4.82182538 Solving -1.5 + x = -4.82182538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -4.82182538 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -4.82182538 + 1.5 x = -4.82182538 + 1.5 Combine like terms: -4.82182538 + 1.5 = -3.32182538 x = -3.32182538 Simplifying x = -3.32182538Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.32182538, -3.32182538}
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