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Simplifying (x + -0.5)(x + -0.5) + -1.561 = 0 Reorder the terms: (-0.5 + x)(x + -0.5) + -1.561 = 0 Reorder the terms: (-0.5 + x)(-0.5 + x) + -1.561 = 0 Multiply (-0.5 + x) * (-0.5 + x) (-0.5(-0.5 + x) + x(-0.5 + x)) + -1.561 = 0 ((-0.5 * -0.5 + x * -0.5) + x(-0.5 + x)) + -1.561 = 0 ((0.25 + -0.5x) + x(-0.5 + x)) + -1.561 = 0 (0.25 + -0.5x + (-0.5 * x + x * x)) + -1.561 = 0 (0.25 + -0.5x + (-0.5x + x2)) + -1.561 = 0 Combine like terms: -0.5x + -0.5x = -1x (0.25 + -1x + x2) + -1.561 = 0 Reorder the terms: 0.25 + -1.561 + -1x + x2 = 0 Combine like terms: 0.25 + -1.561 = -1.311 -1.311 + -1x + x2 = 0 Solving -1.311 + -1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1.311' to each side of the equation. -1.311 + -1x + 1.311 + x2 = 0 + 1.311 Reorder the terms: -1.311 + 1.311 + -1x + x2 = 0 + 1.311 Combine like terms: -1.311 + 1.311 = 0.000 0.000 + -1x + x2 = 0 + 1.311 -1x + x2 = 0 + 1.311 Combine like terms: 0 + 1.311 = 1.311 -1x + x2 = 1.311 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 = 1.311 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 1.311 + 0.25 Combine like terms: 1.311 + 0.25 = 1.561 0.25 + -1x + x2 = 1.561 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 1.561 Calculate the square root of the right side: 1.249399856 Break this problem into two subproblems by setting (x + -0.5) equal to 1.249399856 and -1.249399856.Subproblem 1
x + -0.5 = 1.249399856 Simplifying x + -0.5 = 1.249399856 Reorder the terms: -0.5 + x = 1.249399856 Solving -0.5 + x = 1.249399856 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 = 1.249399856 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.249399856 + 0.5 x = 1.249399856 + 0.5 Combine like terms: 1.249399856 + 0.5 = 1.749399856 x = 1.749399856 Simplifying x = 1.749399856Subproblem 2
x + -0.5 = -1.249399856 Simplifying x + -0.5 = -1.249399856 Reorder the terms: -0.5 + x = -1.249399856 Solving -0.5 + x = -1.249399856 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 = -1.249399856 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.249399856 + 0.5 x = -1.249399856 + 0.5 Combine like terms: -1.249399856 + 0.5 = -0.749399856 x = -0.749399856 Simplifying x = -0.749399856Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.749399856, -0.749399856}
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