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Simplifying x(x + 1) = 97 Reorder the terms: x(1 + x) = 97 (1 * x + x * x) = 97 (1x + x2) = 97 Solving 1x + x2 = 97 Solving for variable 'x'. Reorder the terms: -97 + 1x + x2 = 97 + -97 Combine like terms: 97 + -97 = 0 -97 + 1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '97' to each side of the equation. -97 + 1x + 97 + x2 = 0 + 97 Reorder the terms: -97 + 97 + 1x + x2 = 0 + 97 Combine like terms: -97 + 97 = 0 0 + 1x + x2 = 0 + 97 1x + x2 = 0 + 97 Combine like terms: 0 + 97 = 97 1x + x2 = 97 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 = 97 + 0.25 Reorder the terms: 0.25 + x + x2 = 97 + 0.25 Combine like terms: 97 + 0.25 = 97.25 0.25 + x + x2 = 97.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 97.25 Calculate the square root of the right side: 9.861541462 Break this problem into two subproblems by setting (x + 0.5) equal to 9.861541462 and -9.861541462.Subproblem 1
x + 0.5 = 9.861541462 Simplifying x + 0.5 = 9.861541462 Reorder the terms: 0.5 + x = 9.861541462 Solving 0.5 + x = 9.861541462 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 = 9.861541462 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 9.861541462 + -0.5 x = 9.861541462 + -0.5 Combine like terms: 9.861541462 + -0.5 = 9.361541462 x = 9.361541462 Simplifying x = 9.361541462Subproblem 2
x + 0.5 = -9.861541462 Simplifying x + 0.5 = -9.861541462 Reorder the terms: 0.5 + x = -9.861541462 Solving 0.5 + x = -9.861541462 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 = -9.861541462 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -9.861541462 + -0.5 x = -9.861541462 + -0.5 Combine like terms: -9.861541462 + -0.5 = -10.361541462 x = -10.361541462 Simplifying x = -10.361541462Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.361541462, -10.361541462}
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