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Simplifying (2x + -3) + (x2 + -4x) = 180 Reorder the terms: (-3 + 2x) + (x2 + -4x) = 180 Remove parenthesis around (-3 + 2x) -3 + 2x + (x2 + -4x) = 180 Reorder the terms: -3 + 2x + (-4x + x2) = 180 Remove parenthesis around (-4x + x2) -3 + 2x + -4x + x2 = 180 Combine like terms: 2x + -4x = -2x -3 + -2x + x2 = 180 Solving -3 + -2x + x2 = 180 Solving for variable 'x'. Reorder the terms: -3 + -180 + -2x + x2 = 180 + -180 Combine like terms: -3 + -180 = -183 -183 + -2x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -183 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '183' to each side of the equation. -183 + -2x + 183 + x2 = 0 + 183 Reorder the terms: -183 + 183 + -2x + x2 = 0 + 183 Combine like terms: -183 + 183 = 0 0 + -2x + x2 = 0 + 183 -2x + x2 = 0 + 183 Combine like terms: 0 + 183 = 183 -2x + x2 = 183 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 = 183 + 1 Reorder the terms: 1 + -2x + x2 = 183 + 1 Combine like terms: 183 + 1 = 184 1 + -2x + x2 = 184 Factor a perfect square on the left side: (x + -1)(x + -1) = 184 Calculate the square root of the right side: 13.564659966 Break this problem into two subproblems by setting (x + -1) equal to 13.564659966 and -13.564659966.Subproblem 1
x + -1 = 13.564659966 Simplifying x + -1 = 13.564659966 Reorder the terms: -1 + x = 13.564659966 Solving -1 + x = 13.564659966 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 = 13.564659966 + 1 Combine like terms: -1 + 1 = 0 0 + x = 13.564659966 + 1 x = 13.564659966 + 1 Combine like terms: 13.564659966 + 1 = 14.564659966 x = 14.564659966 Simplifying x = 14.564659966Subproblem 2
x + -1 = -13.564659966 Simplifying x + -1 = -13.564659966 Reorder the terms: -1 + x = -13.564659966 Solving -1 + x = -13.564659966 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 = -13.564659966 + 1 Combine like terms: -1 + 1 = 0 0 + x = -13.564659966 + 1 x = -13.564659966 + 1 Combine like terms: -13.564659966 + 1 = -12.564659966 x = -12.564659966 Simplifying x = -12.564659966Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.564659966, -12.564659966}
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