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Simplifying x2 + -2x + -2186 = 0 Reorder the terms: -2186 + -2x + x2 = 0 Solving -2186 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2186' to each side of the equation. -2186 + -2x + 2186 + x2 = 0 + 2186 Reorder the terms: -2186 + 2186 + -2x + x2 = 0 + 2186 Combine like terms: -2186 + 2186 = 0 0 + -2x + x2 = 0 + 2186 -2x + x2 = 0 + 2186 Combine like terms: 0 + 2186 = 2186 -2x + x2 = 2186 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 = 2186 + 1 Reorder the terms: 1 + -2x + x2 = 2186 + 1 Combine like terms: 2186 + 1 = 2187 1 + -2x + x2 = 2187 Factor a perfect square on the left side: (x + -1)(x + -1) = 2187 Calculate the square root of the right side: 46.765371804 Break this problem into two subproblems by setting (x + -1) equal to 46.765371804 and -46.765371804.Subproblem 1
x + -1 = 46.765371804 Simplifying x + -1 = 46.765371804 Reorder the terms: -1 + x = 46.765371804 Solving -1 + x = 46.765371804 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 = 46.765371804 + 1 Combine like terms: -1 + 1 = 0 0 + x = 46.765371804 + 1 x = 46.765371804 + 1 Combine like terms: 46.765371804 + 1 = 47.765371804 x = 47.765371804 Simplifying x = 47.765371804Subproblem 2
x + -1 = -46.765371804 Simplifying x + -1 = -46.765371804 Reorder the terms: -1 + x = -46.765371804 Solving -1 + x = -46.765371804 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 = -46.765371804 + 1 Combine like terms: -1 + 1 = 0 0 + x = -46.765371804 + 1 x = -46.765371804 + 1 Combine like terms: -46.765371804 + 1 = -45.765371804 x = -45.765371804 Simplifying x = -45.765371804Solution
The solution to the problem is based on the solutions from the subproblems. x = {47.765371804, -45.765371804}
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