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Simplifying x(x + 23) = 87 Reorder the terms: x(23 + x) = 87 (23 * x + x * x) = 87 (23x + x2) = 87 Solving 23x + x2 = 87 Solving for variable 'x'. Reorder the terms: -87 + 23x + x2 = 87 + -87 Combine like terms: 87 + -87 = 0 -87 + 23x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '87' to each side of the equation. -87 + 23x + 87 + x2 = 0 + 87 Reorder the terms: -87 + 87 + 23x + x2 = 0 + 87 Combine like terms: -87 + 87 = 0 0 + 23x + x2 = 0 + 87 23x + x2 = 0 + 87 Combine like terms: 0 + 87 = 87 23x + x2 = 87 The x term is 23x. Take half its coefficient (11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. 23x + 132.25 + x2 = 87 + 132.25 Reorder the terms: 132.25 + 23x + x2 = 87 + 132.25 Combine like terms: 87 + 132.25 = 219.25 132.25 + 23x + x2 = 219.25 Factor a perfect square on the left side: (x + 11.5)(x + 11.5) = 219.25 Calculate the square root of the right side: 14.807092895 Break this problem into two subproblems by setting (x + 11.5) equal to 14.807092895 and -14.807092895.Subproblem 1
x + 11.5 = 14.807092895 Simplifying x + 11.5 = 14.807092895 Reorder the terms: 11.5 + x = 14.807092895 Solving 11.5 + x = 14.807092895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + x = 14.807092895 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = 14.807092895 + -11.5 x = 14.807092895 + -11.5 Combine like terms: 14.807092895 + -11.5 = 3.307092895 x = 3.307092895 Simplifying x = 3.307092895Subproblem 2
x + 11.5 = -14.807092895 Simplifying x + 11.5 = -14.807092895 Reorder the terms: 11.5 + x = -14.807092895 Solving 11.5 + x = -14.807092895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + x = -14.807092895 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + x = -14.807092895 + -11.5 x = -14.807092895 + -11.5 Combine like terms: -14.807092895 + -11.5 = -26.307092895 x = -26.307092895 Simplifying x = -26.307092895Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.307092895, -26.307092895}
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