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Simplifying x2 + 2x + -202 = 0 Reorder the terms: -202 + 2x + x2 = 0 Solving -202 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '202' to each side of the equation. -202 + 2x + 202 + x2 = 0 + 202 Reorder the terms: -202 + 202 + 2x + x2 = 0 + 202 Combine like terms: -202 + 202 = 0 0 + 2x + x2 = 0 + 202 2x + x2 = 0 + 202 Combine like terms: 0 + 202 = 202 2x + x2 = 202 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 = 202 + 1 Reorder the terms: 1 + 2x + x2 = 202 + 1 Combine like terms: 202 + 1 = 203 1 + 2x + x2 = 203 Factor a perfect square on the left side: (x + 1)(x + 1) = 203 Calculate the square root of the right side: 14.247806849 Break this problem into two subproblems by setting (x + 1) equal to 14.247806849 and -14.247806849.Subproblem 1
x + 1 = 14.247806849 Simplifying x + 1 = 14.247806849 Reorder the terms: 1 + x = 14.247806849 Solving 1 + x = 14.247806849 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 = 14.247806849 + -1 Combine like terms: 1 + -1 = 0 0 + x = 14.247806849 + -1 x = 14.247806849 + -1 Combine like terms: 14.247806849 + -1 = 13.247806849 x = 13.247806849 Simplifying x = 13.247806849Subproblem 2
x + 1 = -14.247806849 Simplifying x + 1 = -14.247806849 Reorder the terms: 1 + x = -14.247806849 Solving 1 + x = -14.247806849 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 = -14.247806849 + -1 Combine like terms: 1 + -1 = 0 0 + x = -14.247806849 + -1 x = -14.247806849 + -1 Combine like terms: -14.247806849 + -1 = -15.247806849 x = -15.247806849 Simplifying x = -15.247806849Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.247806849, -15.247806849}
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