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Simplifying (x2 + -2x) + -180 = 0 Reorder the terms: (-2x + x2) + -180 = 0 Remove parenthesis around (-2x + x2) -2x + x2 + -180 = 0 Reorder the terms: -180 + -2x + x2 = 0 Solving -180 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + -2x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + -2x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + -2x + x2 = 0 + 180 -2x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 -2x + x2 = 180 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 = 180 + 1 Reorder the terms: 1 + -2x + x2 = 180 + 1 Combine like terms: 180 + 1 = 181 1 + -2x + x2 = 181 Factor a perfect square on the left side: (x + -1)(x + -1) = 181 Calculate the square root of the right side: 13.453624047 Break this problem into two subproblems by setting (x + -1) equal to 13.453624047 and -13.453624047.Subproblem 1
x + -1 = 13.453624047 Simplifying x + -1 = 13.453624047 Reorder the terms: -1 + x = 13.453624047 Solving -1 + x = 13.453624047 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 = 13.453624047 + 1 Combine like terms: -1 + 1 = 0 0 + x = 13.453624047 + 1 x = 13.453624047 + 1 Combine like terms: 13.453624047 + 1 = 14.453624047 x = 14.453624047 Simplifying x = 14.453624047Subproblem 2
x + -1 = -13.453624047 Simplifying x + -1 = -13.453624047 Reorder the terms: -1 + x = -13.453624047 Solving -1 + x = -13.453624047 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 = -13.453624047 + 1 Combine like terms: -1 + 1 = 0 0 + x = -13.453624047 + 1 x = -13.453624047 + 1 Combine like terms: -13.453624047 + 1 = -12.453624047 x = -12.453624047 Simplifying x = -12.453624047Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.453624047, -12.453624047}
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