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Simplifying x2 + 2x = 869 Reorder the terms: 2x + x2 = 869 Solving 2x + x2 = 869 Solving for variable 'x'. Reorder the terms: -869 + 2x + x2 = 869 + -869 Combine like terms: 869 + -869 = 0 -869 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '869' to each side of the equation. -869 + 2x + 869 + x2 = 0 + 869 Reorder the terms: -869 + 869 + 2x + x2 = 0 + 869 Combine like terms: -869 + 869 = 0 0 + 2x + x2 = 0 + 869 2x + x2 = 0 + 869 Combine like terms: 0 + 869 = 869 2x + x2 = 869 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 = 869 + 1 Reorder the terms: 1 + 2x + x2 = 869 + 1 Combine like terms: 869 + 1 = 870 1 + 2x + x2 = 870 Factor a perfect square on the left side: (x + 1)(x + 1) = 870 Calculate the square root of the right side: 29.495762408 Break this problem into two subproblems by setting (x + 1) equal to 29.495762408 and -29.495762408.Subproblem 1
x + 1 = 29.495762408 Simplifying x + 1 = 29.495762408 Reorder the terms: 1 + x = 29.495762408 Solving 1 + x = 29.495762408 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 = 29.495762408 + -1 Combine like terms: 1 + -1 = 0 0 + x = 29.495762408 + -1 x = 29.495762408 + -1 Combine like terms: 29.495762408 + -1 = 28.495762408 x = 28.495762408 Simplifying x = 28.495762408Subproblem 2
x + 1 = -29.495762408 Simplifying x + 1 = -29.495762408 Reorder the terms: 1 + x = -29.495762408 Solving 1 + x = -29.495762408 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 = -29.495762408 + -1 Combine like terms: 1 + -1 = 0 0 + x = -29.495762408 + -1 x = -29.495762408 + -1 Combine like terms: -29.495762408 + -1 = -30.495762408 x = -30.495762408 Simplifying x = -30.495762408Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.495762408, -30.495762408}
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