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Simplifying x(x + 2) = 97 Reorder the terms: x(2 + x) = 97 (2 * x + x * x) = 97 (2x + x2) = 97 Solving 2x + x2 = 97 Solving for variable 'x'. Reorder the terms: -97 + 2x + x2 = 97 + -97 Combine like terms: 97 + -97 = 0 -97 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '97' to each side of the equation. -97 + 2x + 97 + x2 = 0 + 97 Reorder the terms: -97 + 97 + 2x + x2 = 0 + 97 Combine like terms: -97 + 97 = 0 0 + 2x + x2 = 0 + 97 2x + x2 = 0 + 97 Combine like terms: 0 + 97 = 97 2x + x2 = 97 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 97 + 1 Reorder the terms: 1 + 2x + x2 = 97 + 1 Combine like terms: 97 + 1 = 98 1 + 2x + x2 = 98 Factor a perfect square on the left side: (x + 1)(x + 1) = 98 Calculate the square root of the right side: 9.899494937 Break this problem into two subproblems by setting (x + 1) equal to 9.899494937 and -9.899494937.Subproblem 1
x + 1 = 9.899494937 Simplifying x + 1 = 9.899494937 Reorder the terms: 1 + x = 9.899494937 Solving 1 + x = 9.899494937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 9.899494937 + -1 Combine like terms: 1 + -1 = 0 0 + x = 9.899494937 + -1 x = 9.899494937 + -1 Combine like terms: 9.899494937 + -1 = 8.899494937 x = 8.899494937 Simplifying x = 8.899494937Subproblem 2
x + 1 = -9.899494937 Simplifying x + 1 = -9.899494937 Reorder the terms: 1 + x = -9.899494937 Solving 1 + x = -9.899494937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -9.899494937 + -1 Combine like terms: 1 + -1 = 0 0 + x = -9.899494937 + -1 x = -9.899494937 + -1 Combine like terms: -9.899494937 + -1 = -10.899494937 x = -10.899494937 Simplifying x = -10.899494937Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.899494937, -10.899494937}
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