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Simplifying 180 = 0.5x2 + 2x + 2 Reorder the terms: 180 = 2 + 2x + 0.5x2 Solving 180 = 2 + 2x + 0.5x2 Solving for variable 'x'. Combine like terms: 180 + -2 = 178 178 + -2x + -0.5x2 = 2 + 2x + 0.5x2 + -2 + -2x + -0.5x2 Reorder the terms: 178 + -2x + -0.5x2 = 2 + -2 + 2x + -2x + 0.5x2 + -0.5x2 Combine like terms: 2 + -2 = 0 178 + -2x + -0.5x2 = 0 + 2x + -2x + 0.5x2 + -0.5x2 178 + -2x + -0.5x2 = 2x + -2x + 0.5x2 + -0.5x2 Combine like terms: 2x + -2x = 0 178 + -2x + -0.5x2 = 0 + 0.5x2 + -0.5x2 178 + -2x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 178 + -2x + -0.5x2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -356 + 4x + x2 = 0 Move the constant term to the right: Add '356' to each side of the equation. -356 + 4x + 356 + x2 = 0 + 356 Reorder the terms: -356 + 356 + 4x + x2 = 0 + 356 Combine like terms: -356 + 356 = 0 0 + 4x + x2 = 0 + 356 4x + x2 = 0 + 356 Combine like terms: 0 + 356 = 356 4x + x2 = 356 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 356 + 4 Reorder the terms: 4 + 4x + x2 = 356 + 4 Combine like terms: 356 + 4 = 360 4 + 4x + x2 = 360 Factor a perfect square on the left side: (x + 2)(x + 2) = 360 Calculate the square root of the right side: 18.973665961 Break this problem into two subproblems by setting (x + 2) equal to 18.973665961 and -18.973665961.Subproblem 1
x + 2 = 18.973665961 Simplifying x + 2 = 18.973665961 Reorder the terms: 2 + x = 18.973665961 Solving 2 + x = 18.973665961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 18.973665961 + -2 Combine like terms: 2 + -2 = 0 0 + x = 18.973665961 + -2 x = 18.973665961 + -2 Combine like terms: 18.973665961 + -2 = 16.973665961 x = 16.973665961 Simplifying x = 16.973665961Subproblem 2
x + 2 = -18.973665961 Simplifying x + 2 = -18.973665961 Reorder the terms: 2 + x = -18.973665961 Solving 2 + x = -18.973665961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -18.973665961 + -2 Combine like terms: 2 + -2 = 0 0 + x = -18.973665961 + -2 x = -18.973665961 + -2 Combine like terms: -18.973665961 + -2 = -20.973665961 x = -20.973665961 Simplifying x = -20.973665961Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.973665961, -20.973665961}
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