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Simplifying (x)(x + 1) = 85 Reorder the terms: x(1 + x) = 85 (1 * x + x * x) = 85 (1x + x2) = 85 Solving 1x + x2 = 85 Solving for variable 'x'. Reorder the terms: -85 + 1x + x2 = 85 + -85 Combine like terms: 85 + -85 = 0 -85 + 1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '85' to each side of the equation. -85 + 1x + 85 + x2 = 0 + 85 Reorder the terms: -85 + 85 + 1x + x2 = 0 + 85 Combine like terms: -85 + 85 = 0 0 + 1x + x2 = 0 + 85 1x + x2 = 0 + 85 Combine like terms: 0 + 85 = 85 1x + x2 = 85 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 = 85 + 0.25 Reorder the terms: 0.25 + x + x2 = 85 + 0.25 Combine like terms: 85 + 0.25 = 85.25 0.25 + x + x2 = 85.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 85.25 Calculate the square root of the right side: 9.233092656 Break this problem into two subproblems by setting (x + 0.5) equal to 9.233092656 and -9.233092656.Subproblem 1
x + 0.5 = 9.233092656 Simplifying x + 0.5 = 9.233092656 Reorder the terms: 0.5 + x = 9.233092656 Solving 0.5 + x = 9.233092656 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 = 9.233092656 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 9.233092656 + -0.5 x = 9.233092656 + -0.5 Combine like terms: 9.233092656 + -0.5 = 8.733092656 x = 8.733092656 Simplifying x = 8.733092656Subproblem 2
x + 0.5 = -9.233092656 Simplifying x + 0.5 = -9.233092656 Reorder the terms: 0.5 + x = -9.233092656 Solving 0.5 + x = -9.233092656 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 = -9.233092656 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -9.233092656 + -0.5 x = -9.233092656 + -0.5 Combine like terms: -9.233092656 + -0.5 = -9.733092656 x = -9.733092656 Simplifying x = -9.733092656Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.733092656, -9.733092656}
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