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Simplifying x(x + 1) = 89 Reorder the terms: x(1 + x) = 89 (1 * x + x * x) = 89 (1x + x2) = 89 Solving 1x + x2 = 89 Solving for variable 'x'. Reorder the terms: -89 + 1x + x2 = 89 + -89 Combine like terms: 89 + -89 = 0 -89 + 1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '89' to each side of the equation. -89 + 1x + 89 + x2 = 0 + 89 Reorder the terms: -89 + 89 + 1x + x2 = 0 + 89 Combine like terms: -89 + 89 = 0 0 + 1x + x2 = 0 + 89 1x + x2 = 0 + 89 Combine like terms: 0 + 89 = 89 1x + x2 = 89 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. x + 0.25 + x2 = 89 + 0.25 Reorder the terms: 0.25 + x + x2 = 89 + 0.25 Combine like terms: 89 + 0.25 = 89.25 0.25 + x + x2 = 89.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 89.25 Calculate the square root of the right side: 9.447221814 Break this problem into two subproblems by setting (x + 0.5) equal to 9.447221814 and -9.447221814.Subproblem 1
x + 0.5 = 9.447221814 Simplifying x + 0.5 = 9.447221814 Reorder the terms: 0.5 + x = 9.447221814 Solving 0.5 + x = 9.447221814 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 = 9.447221814 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 9.447221814 + -0.5 x = 9.447221814 + -0.5 Combine like terms: 9.447221814 + -0.5 = 8.947221814 x = 8.947221814 Simplifying x = 8.947221814Subproblem 2
x + 0.5 = -9.447221814 Simplifying x + 0.5 = -9.447221814 Reorder the terms: 0.5 + x = -9.447221814 Solving 0.5 + x = -9.447221814 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 = -9.447221814 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -9.447221814 + -0.5 x = -9.447221814 + -0.5 Combine like terms: -9.447221814 + -0.5 = -9.947221814 x = -9.947221814 Simplifying x = -9.947221814Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.947221814, -9.947221814}
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