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Simplifying 180 = (X2 + -4) + (4 + -2X) Reorder the terms: 180 = (-4 + X2) + (4 + -2X) Remove parenthesis around (-4 + X2) 180 = -4 + X2 + (4 + -2X) Remove parenthesis around (4 + -2X) 180 = -4 + X2 + 4 + -2X Reorder the terms: 180 = -4 + 4 + -2X + X2 Combine like terms: -4 + 4 = 0 180 = 0 + -2X + X2 180 = -2X + X2 Solving 180 = -2X + X2 Solving for variable 'X'. Reorder the terms: 180 + 2X + -1X2 = -2X + 2X + X2 + -1X2 Combine like terms: -2X + 2X = 0 180 + 2X + -1X2 = 0 + X2 + -1X2 180 + 2X + -1X2 = X2 + -1X2 Combine like terms: X2 + -1X2 = 0 180 + 2X + -1X2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -180 + -2X + X2 = 0 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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