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Simplifying x + 5 + -1(9 + -1x)(9 + x) = 0 Multiply (9 + -1x) * (9 + x) x + 5 + -1(9(9 + x) + -1x * (9 + x)) = 0 x + 5 + -1((9 * 9 + x * 9) + -1x * (9 + x)) = 0 x + 5 + -1((81 + 9x) + -1x * (9 + x)) = 0 x + 5 + -1(81 + 9x + (9 * -1x + x * -1x)) = 0 x + 5 + -1(81 + 9x + (-9x + -1x2)) = 0 Combine like terms: 9x + -9x = 0 x + 5 + -1(81 + 0 + -1x2) = 0 x + 5 + -1(81 + -1x2) = 0 x + 5 + (81 * -1 + -1x2 * -1) = 0 x + 5 + (-81 + 1x2) = 0 Reorder the terms: 5 + -81 + x + 1x2 = 0 Combine like terms: 5 + -81 = -76 -76 + x + 1x2 = 0 Solving -76 + x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '76' to each side of the equation. -76 + x + 76 + x2 = 0 + 76 Reorder the terms: -76 + 76 + x + x2 = 0 + 76 Combine like terms: -76 + 76 = 0 0 + x + x2 = 0 + 76 x + x2 = 0 + 76 Combine like terms: 0 + 76 = 76 x + x2 = 76 The x term is x. 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. x + 0.25 + x2 = 76 + 0.25 Reorder the terms: 0.25 + x + x2 = 76 + 0.25 Combine like terms: 76 + 0.25 = 76.25 0.25 + x + x2 = 76.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 76.25 Calculate the square root of the right side: 8.732124598 Break this problem into two subproblems by setting (x + 0.5) equal to 8.732124598 and -8.732124598.Subproblem 1
x + 0.5 = 8.732124598 Simplifying x + 0.5 = 8.732124598 Reorder the terms: 0.5 + x = 8.732124598 Solving 0.5 + x = 8.732124598 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 = 8.732124598 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 8.732124598 + -0.5 x = 8.732124598 + -0.5 Combine like terms: 8.732124598 + -0.5 = 8.232124598 x = 8.232124598 Simplifying x = 8.232124598Subproblem 2
x + 0.5 = -8.732124598 Simplifying x + 0.5 = -8.732124598 Reorder the terms: 0.5 + x = -8.732124598 Solving 0.5 + x = -8.732124598 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 = -8.732124598 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -8.732124598 + -0.5 x = -8.732124598 + -0.5 Combine like terms: -8.732124598 + -0.5 = -9.232124598 x = -9.232124598 Simplifying x = -9.232124598Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.232124598, -9.232124598}
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