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Simplifying 210.80 = (15 + x)(10 + -0.20x) Multiply (15 + x) * (10 + -0.20x) 210.80 = (15(10 + -0.20x) + x(10 + -0.20x)) 210.80 = ((10 * 15 + -0.20x * 15) + x(10 + -0.20x)) 210.80 = ((150 + -3x) + x(10 + -0.20x)) 210.80 = (150 + -3x + (10 * x + -0.20x * x)) 210.80 = (150 + -3x + (10x + -0.20x2)) Combine like terms: -3x + 10x = 7x 210.80 = (150 + 7x + -0.20x2) Solving 210.80 = 150 + 7x + -0.20x2 Solving for variable 'x'. Combine like terms: 210.80 + -150 = 60.8 60.8 + -7x + 0.20x2 = 150 + 7x + -0.20x2 + -150 + -7x + 0.20x2 Reorder the terms: 60.8 + -7x + 0.20x2 = 150 + -150 + 7x + -7x + -0.20x2 + 0.20x2 Combine like terms: 150 + -150 = 0 60.8 + -7x + 0.20x2 = 0 + 7x + -7x + -0.20x2 + 0.20x2 60.8 + -7x + 0.20x2 = 7x + -7x + -0.20x2 + 0.20x2 Combine like terms: 7x + -7x = 0 60.8 + -7x + 0.20x2 = 0 + -0.20x2 + 0.20x2 60.8 + -7x + 0.20x2 = -0.20x2 + 0.20x2 Combine like terms: -0.20x2 + 0.20x2 = 0.00 60.8 + -7x + 0.20x2 = 0.00 Begin completing the square. Divide all terms by 0.20 the coefficient of the squared term: Divide each side by '0.20'. 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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