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Simplifying x2 + 2x = 65 Reorder the terms: 2x + x2 = 65 Solving 2x + x2 = 65 Solving for variable 'x'. Reorder the terms: -65 + 2x + x2 = 65 + -65 Combine like terms: 65 + -65 = 0 -65 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '65' to each side of the equation. -65 + 2x + 65 + x2 = 0 + 65 Reorder the terms: -65 + 65 + 2x + x2 = 0 + 65 Combine like terms: -65 + 65 = 0 0 + 2x + x2 = 0 + 65 2x + x2 = 0 + 65 Combine like terms: 0 + 65 = 65 2x + x2 = 65 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 = 65 + 1 Reorder the terms: 1 + 2x + x2 = 65 + 1 Combine like terms: 65 + 1 = 66 1 + 2x + x2 = 66 Factor a perfect square on the left side: (x + 1)(x + 1) = 66 Calculate the square root of the right side: 8.124038405 Break this problem into two subproblems by setting (x + 1) equal to 8.124038405 and -8.124038405.Subproblem 1
x + 1 = 8.124038405 Simplifying x + 1 = 8.124038405 Reorder the terms: 1 + x = 8.124038405 Solving 1 + x = 8.124038405 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 = 8.124038405 + -1 Combine like terms: 1 + -1 = 0 0 + x = 8.124038405 + -1 x = 8.124038405 + -1 Combine like terms: 8.124038405 + -1 = 7.124038405 x = 7.124038405 Simplifying x = 7.124038405Subproblem 2
x + 1 = -8.124038405 Simplifying x + 1 = -8.124038405 Reorder the terms: 1 + x = -8.124038405 Solving 1 + x = -8.124038405 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 = -8.124038405 + -1 Combine like terms: 1 + -1 = 0 0 + x = -8.124038405 + -1 x = -8.124038405 + -1 Combine like terms: -8.124038405 + -1 = -9.124038405 x = -9.124038405 Simplifying x = -9.124038405Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.124038405, -9.124038405}
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