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Simplifying x(x + 2) = 76 Reorder the terms: x(2 + x) = 76 (2 * x + x * x) = 76 (2x + x2) = 76 Solving 2x + x2 = 76 Solving for variable 'x'. Reorder the terms: -76 + 2x + x2 = 76 + -76 Combine like terms: 76 + -76 = 0 -76 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '76' to each side of the equation. -76 + 2x + 76 + x2 = 0 + 76 Reorder the terms: -76 + 76 + 2x + x2 = 0 + 76 Combine like terms: -76 + 76 = 0 0 + 2x + x2 = 0 + 76 2x + x2 = 0 + 76 Combine like terms: 0 + 76 = 76 2x + x2 = 76 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 = 76 + 1 Reorder the terms: 1 + 2x + x2 = 76 + 1 Combine like terms: 76 + 1 = 77 1 + 2x + x2 = 77 Factor a perfect square on the left side: (x + 1)(x + 1) = 77 Calculate the square root of the right side: 8.774964387 Break this problem into two subproblems by setting (x + 1) equal to 8.774964387 and -8.774964387.Subproblem 1
x + 1 = 8.774964387 Simplifying x + 1 = 8.774964387 Reorder the terms: 1 + x = 8.774964387 Solving 1 + x = 8.774964387 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 = 8.774964387 + -1 Combine like terms: 1 + -1 = 0 0 + x = 8.774964387 + -1 x = 8.774964387 + -1 Combine like terms: 8.774964387 + -1 = 7.774964387 x = 7.774964387 Simplifying x = 7.774964387Subproblem 2
x + 1 = -8.774964387 Simplifying x + 1 = -8.774964387 Reorder the terms: 1 + x = -8.774964387 Solving 1 + x = -8.774964387 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 = -8.774964387 + -1 Combine like terms: 1 + -1 = 0 0 + x = -8.774964387 + -1 x = -8.774964387 + -1 Combine like terms: -8.774964387 + -1 = -9.774964387 x = -9.774964387 Simplifying x = -9.774964387Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.774964387, -9.774964387}
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