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Simplifying x2 + 2x + -49 = 169 Reorder the terms: -49 + 2x + x2 = 169 Solving -49 + 2x + x2 = 169 Solving for variable 'x'. Reorder the terms: -49 + -169 + 2x + x2 = 169 + -169 Combine like terms: -49 + -169 = -218 -218 + 2x + x2 = 169 + -169 Combine like terms: 169 + -169 = 0 -218 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '218' to each side of the equation. -218 + 2x + 218 + x2 = 0 + 218 Reorder the terms: -218 + 218 + 2x + x2 = 0 + 218 Combine like terms: -218 + 218 = 0 0 + 2x + x2 = 0 + 218 2x + x2 = 0 + 218 Combine like terms: 0 + 218 = 218 2x + x2 = 218 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 = 218 + 1 Reorder the terms: 1 + 2x + x2 = 218 + 1 Combine like terms: 218 + 1 = 219 1 + 2x + x2 = 219 Factor a perfect square on the left side: (x + 1)(x + 1) = 219 Calculate the square root of the right side: 14.798648587 Break this problem into two subproblems by setting (x + 1) equal to 14.798648587 and -14.798648587.Subproblem 1
x + 1 = 14.798648587 Simplifying x + 1 = 14.798648587 Reorder the terms: 1 + x = 14.798648587 Solving 1 + x = 14.798648587 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 = 14.798648587 + -1 Combine like terms: 1 + -1 = 0 0 + x = 14.798648587 + -1 x = 14.798648587 + -1 Combine like terms: 14.798648587 + -1 = 13.798648587 x = 13.798648587 Simplifying x = 13.798648587Subproblem 2
x + 1 = -14.798648587 Simplifying x + 1 = -14.798648587 Reorder the terms: 1 + x = -14.798648587 Solving 1 + x = -14.798648587 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 = -14.798648587 + -1 Combine like terms: 1 + -1 = 0 0 + x = -14.798648587 + -1 x = -14.798648587 + -1 Combine like terms: -14.798648587 + -1 = -15.798648587 x = -15.798648587 Simplifying x = -15.798648587Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.798648587, -15.798648587}
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