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Simplifying (x + -2)(x + -1) + -2.50x + -0.42 = 0 Reorder the terms: (-2 + x)(x + -1) + -2.50x + -0.42 = 0 Reorder the terms: (-2 + x)(-1 + x) + -2.50x + -0.42 = 0 Multiply (-2 + x) * (-1 + x) (-2(-1 + x) + x(-1 + x)) + -2.50x + -0.42 = 0 ((-1 * -2 + x * -2) + x(-1 + x)) + -2.50x + -0.42 = 0 ((2 + -2x) + x(-1 + x)) + -2.50x + -0.42 = 0 (2 + -2x + (-1 * x + x * x)) + -2.50x + -0.42 = 0 (2 + -2x + (-1x + x2)) + -2.50x + -0.42 = 0 Combine like terms: -2x + -1x = -3x (2 + -3x + x2) + -2.50x + -0.42 = 0 Reorder the terms: 2 + -0.42 + -3x + -2.50x + x2 = 0 Combine like terms: 2 + -0.42 = 1.58 1.58 + -3x + -2.50x + x2 = 0 Combine like terms: -3x + -2.50x = -5.5x 1.58 + -5.5x + x2 = 0 Solving 1.58 + -5.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1.58' to each side of the equation. 1.58 + -5.5x + -1.58 + x2 = 0 + -1.58 Reorder the terms: 1.58 + -1.58 + -5.5x + x2 = 0 + -1.58 Combine like terms: 1.58 + -1.58 = 0.00 0.00 + -5.5x + x2 = 0 + -1.58 -5.5x + x2 = 0 + -1.58 Combine like terms: 0 + -1.58 = -1.58 -5.5x + x2 = -1.58 The x term is -5.5x. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5x + 7.5625 + x2 = -1.58 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = -1.58 + 7.5625 Combine like terms: -1.58 + 7.5625 = 5.9825 7.5625 + -5.5x + x2 = 5.9825 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 5.9825 Calculate the square root of the right side: 2.445914962 Break this problem into two subproblems by setting (x + -2.75) equal to 2.445914962 and -2.445914962.Subproblem 1
x + -2.75 = 2.445914962 Simplifying x + -2.75 = 2.445914962 Reorder the terms: -2.75 + x = 2.445914962 Solving -2.75 + x = 2.445914962 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 2.445914962 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 2.445914962 + 2.75 x = 2.445914962 + 2.75 Combine like terms: 2.445914962 + 2.75 = 5.195914962 x = 5.195914962 Simplifying x = 5.195914962Subproblem 2
x + -2.75 = -2.445914962 Simplifying x + -2.75 = -2.445914962 Reorder the terms: -2.75 + x = -2.445914962 Solving -2.75 + x = -2.445914962 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -2.445914962 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -2.445914962 + 2.75 x = -2.445914962 + 2.75 Combine like terms: -2.445914962 + 2.75 = 0.304085038 x = 0.304085038 Simplifying x = 0.304085038Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.195914962, 0.304085038}
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