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Simplifying (500 + -25x)(2 + 0.25x) = 0 Multiply (500 + -25x) * (2 + 0.25x) (500(2 + 0.25x) + -25x * (2 + 0.25x)) = 0 ((2 * 500 + 0.25x * 500) + -25x * (2 + 0.25x)) = 0 ((1000 + 125x) + -25x * (2 + 0.25x)) = 0 (1000 + 125x + (2 * -25x + 0.25x * -25x)) = 0 (1000 + 125x + (-50x + -6.25x2)) = 0 Combine like terms: 125x + -50x = 75x (1000 + 75x + -6.25x2) = 0 Solving 1000 + 75x + -6.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -6.25 the coefficient of the squared term: Divide each side by '-6.25'. -160 + -12x + x2 = 0 Move the constant term to the right: Add '160' to each side of the equation. -160 + -12x + 160 + x2 = 0 + 160 Reorder the terms: -160 + 160 + -12x + x2 = 0 + 160 Combine like terms: -160 + 160 = 0 0 + -12x + x2 = 0 + 160 -12x + x2 = 0 + 160 Combine like terms: 0 + 160 = 160 -12x + x2 = 160 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 160 + 36 Reorder the terms: 36 + -12x + x2 = 160 + 36 Combine like terms: 160 + 36 = 196 36 + -12x + x2 = 196 Factor a perfect square on the left side: (x + -6)(x + -6) = 196 Calculate the square root of the right side: 14 Break this problem into two subproblems by setting (x + -6) equal to 14 and -14.Subproblem 1
x + -6 = 14 Simplifying x + -6 = 14 Reorder the terms: -6 + x = 14 Solving -6 + x = 14 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 14 + 6 Combine like terms: -6 + 6 = 0 0 + x = 14 + 6 x = 14 + 6 Combine like terms: 14 + 6 = 20 x = 20 Simplifying x = 20Subproblem 2
x + -6 = -14 Simplifying x + -6 = -14 Reorder the terms: -6 + x = -14 Solving -6 + x = -14 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -14 + 6 Combine like terms: -6 + 6 = 0 0 + x = -14 + 6 x = -14 + 6 Combine like terms: -14 + 6 = -8 x = -8 Simplifying x = -8Solution
The solution to the problem is based on the solutions from the subproblems. x = {20, -8}
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