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Simplifying -0.2x2 + 7x + 150 = 210.8 Reorder the terms: 150 + 7x + -0.2x2 = 210.8 Solving 150 + 7x + -0.2x2 = 210.8 Solving for variable 'x'. Reorder the terms: 150 + -210.8 + 7x + -0.2x2 = 210.8 + -210.8 Combine like terms: 150 + -210.8 = -60.8 -60.8 + 7x + -0.2x2 = 210.8 + -210.8 Combine like terms: 210.8 + -210.8 = 0.0 -60.8 + 7x + -0.2x2 = 0.0 Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. 304 + -35x + x2 = 0 Move the constant term to the right: Add '-304' to each side of the equation. 304 + -35x + -304 + x2 = 0 + -304 Reorder the terms: 304 + -304 + -35x + x2 = 0 + -304 Combine like terms: 304 + -304 = 0 0 + -35x + x2 = 0 + -304 -35x + x2 = 0 + -304 Combine like terms: 0 + -304 = -304 -35x + x2 = -304 The x term is -35x. Take half its coefficient (-17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. -35x + 306.25 + x2 = -304 + 306.25 Reorder the terms: 306.25 + -35x + x2 = -304 + 306.25 Combine like terms: -304 + 306.25 = 2.25 306.25 + -35x + x2 = 2.25 Factor a perfect square on the left side: (x + -17.5)(x + -17.5) = 2.25 Calculate the square root of the right side: 1.5 Break this problem into two subproblems by setting (x + -17.5) equal to 1.5 and -1.5.Subproblem 1
x + -17.5 = 1.5 Simplifying x + -17.5 = 1.5 Reorder the terms: -17.5 + x = 1.5 Solving -17.5 + x = 1.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + x = 1.5 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = 1.5 + 17.5 x = 1.5 + 17.5 Combine like terms: 1.5 + 17.5 = 19 x = 19 Simplifying x = 19Subproblem 2
x + -17.5 = -1.5 Simplifying x + -17.5 = -1.5 Reorder the terms: -17.5 + x = -1.5 Solving -17.5 + x = -1.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + x = -1.5 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = -1.5 + 17.5 x = -1.5 + 17.5 Combine like terms: -1.5 + 17.5 = 16 x = 16 Simplifying x = 16Solution
The solution to the problem is based on the solutions from the subproblems. x = {19, 16}
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