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Simplifying x + (2 + -1x)(2 + -1x) = 81 Multiply (2 + -1x) * (2 + -1x) x + (2(2 + -1x) + -1x * (2 + -1x)) = 81 x + ((2 * 2 + -1x * 2) + -1x * (2 + -1x)) = 81 x + ((4 + -2x) + -1x * (2 + -1x)) = 81 x + (4 + -2x + (2 * -1x + -1x * -1x)) = 81 x + (4 + -2x + (-2x + 1x2)) = 81 Combine like terms: -2x + -2x = -4x x + (4 + -4x + 1x2) = 81 Reorder the terms: 4 + x + -4x + 1x2 = 81 Combine like terms: x + -4x = -3x 4 + -3x + 1x2 = 81 Solving 4 + -3x + 1x2 = 81 Solving for variable 'x'. Reorder the terms: 4 + -81 + -3x + 1x2 = 81 + -81 Combine like terms: 4 + -81 = -77 -77 + -3x + 1x2 = 81 + -81 Combine like terms: 81 + -81 = 0 -77 + -3x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '77' to each side of the equation. -77 + -3x + 77 + x2 = 0 + 77 Reorder the terms: -77 + 77 + -3x + x2 = 0 + 77 Combine like terms: -77 + 77 = 0 0 + -3x + x2 = 0 + 77 -3x + x2 = 0 + 77 Combine like terms: 0 + 77 = 77 -3x + x2 = 77 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 = 77 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 77 + 2.25 Combine like terms: 77 + 2.25 = 79.25 2.25 + -3x + x2 = 79.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 79.25 Calculate the square root of the right side: 8.902246907 Break this problem into two subproblems by setting (x + -1.5) equal to 8.902246907 and -8.902246907.Subproblem 1
x + -1.5 = 8.902246907 Simplifying x + -1.5 = 8.902246907 Reorder the terms: -1.5 + x = 8.902246907 Solving -1.5 + x = 8.902246907 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 = 8.902246907 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 8.902246907 + 1.5 x = 8.902246907 + 1.5 Combine like terms: 8.902246907 + 1.5 = 10.402246907 x = 10.402246907 Simplifying x = 10.402246907Subproblem 2
x + -1.5 = -8.902246907 Simplifying x + -1.5 = -8.902246907 Reorder the terms: -1.5 + x = -8.902246907 Solving -1.5 + x = -8.902246907 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 = -8.902246907 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -8.902246907 + 1.5 x = -8.902246907 + 1.5 Combine like terms: -8.902246907 + 1.5 = -7.402246907 x = -7.402246907 Simplifying x = -7.402246907Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.402246907, -7.402246907}
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