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Simplifying x2 + 2x = 75 Reorder the terms: 2x + x2 = 75 Solving 2x + x2 = 75 Solving for variable 'x'. Reorder the terms: -75 + 2x + x2 = 75 + -75 Combine like terms: 75 + -75 = 0 -75 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '75' to each side of the equation. -75 + 2x + 75 + x2 = 0 + 75 Reorder the terms: -75 + 75 + 2x + x2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + 2x + x2 = 0 + 75 2x + x2 = 0 + 75 Combine like terms: 0 + 75 = 75 2x + x2 = 75 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 = 75 + 1 Reorder the terms: 1 + 2x + x2 = 75 + 1 Combine like terms: 75 + 1 = 76 1 + 2x + x2 = 76 Factor a perfect square on the left side: (x + 1)(x + 1) = 76 Calculate the square root of the right side: 8.717797887 Break this problem into two subproblems by setting (x + 1) equal to 8.717797887 and -8.717797887.Subproblem 1
x + 1 = 8.717797887 Simplifying x + 1 = 8.717797887 Reorder the terms: 1 + x = 8.717797887 Solving 1 + x = 8.717797887 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 = 8.717797887 + -1 Combine like terms: 1 + -1 = 0 0 + x = 8.717797887 + -1 x = 8.717797887 + -1 Combine like terms: 8.717797887 + -1 = 7.717797887 x = 7.717797887 Simplifying x = 7.717797887Subproblem 2
x + 1 = -8.717797887 Simplifying x + 1 = -8.717797887 Reorder the terms: 1 + x = -8.717797887 Solving 1 + x = -8.717797887 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 = -8.717797887 + -1 Combine like terms: 1 + -1 = 0 0 + x = -8.717797887 + -1 x = -8.717797887 + -1 Combine like terms: -8.717797887 + -1 = -9.717797887 x = -9.717797887 Simplifying x = -9.717797887Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.717797887, -9.717797887}
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