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Simplifying (150 + x)(15 + -0.05x) = 0 Multiply (150 + x) * (15 + -0.05x) (150(15 + -0.05x) + x(15 + -0.05x)) = 0 ((15 * 150 + -0.05x * 150) + x(15 + -0.05x)) = 0 ((2250 + -7.5x) + x(15 + -0.05x)) = 0 (2250 + -7.5x + (15 * x + -0.05x * x)) = 0 (2250 + -7.5x + (15x + -0.05x2)) = 0 Combine like terms: -7.5x + 15x = 7.5x (2250 + 7.5x + -0.05x2) = 0 Solving 2250 + 7.5x + -0.05x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.05 the coefficient of the squared term: Divide each side by '-0.05'. -45000 + -150x + x2 = 0 Move the constant term to the right: Add '45000' to each side of the equation. -45000 + -150x + 45000 + x2 = 0 + 45000 Reorder the terms: -45000 + 45000 + -150x + x2 = 0 + 45000 Combine like terms: -45000 + 45000 = 0 0 + -150x + x2 = 0 + 45000 -150x + x2 = 0 + 45000 Combine like terms: 0 + 45000 = 45000 -150x + x2 = 45000 The x term is -150x. Take half its coefficient (-75). Square it (5625) and add it to both sides. Add '5625' to each side of the equation. -150x + 5625 + x2 = 45000 + 5625 Reorder the terms: 5625 + -150x + x2 = 45000 + 5625 Combine like terms: 45000 + 5625 = 50625 5625 + -150x + x2 = 50625 Factor a perfect square on the left side: (x + -75)(x + -75) = 50625 Calculate the square root of the right side: 225 Break this problem into two subproblems by setting (x + -75) equal to 225 and -225.Subproblem 1
x + -75 = 225 Simplifying x + -75 = 225 Reorder the terms: -75 + x = 225 Solving -75 + x = 225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '75' to each side of the equation. -75 + 75 + x = 225 + 75 Combine like terms: -75 + 75 = 0 0 + x = 225 + 75 x = 225 + 75 Combine like terms: 225 + 75 = 300 x = 300 Simplifying x = 300Subproblem 2
x + -75 = -225 Simplifying x + -75 = -225 Reorder the terms: -75 + x = -225 Solving -75 + x = -225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '75' to each side of the equation. -75 + 75 + x = -225 + 75 Combine like terms: -75 + 75 = 0 0 + x = -225 + 75 x = -225 + 75 Combine like terms: -225 + 75 = -150 x = -150 Simplifying x = -150Solution
The solution to the problem is based on the solutions from the subproblems. x = {300, -150}
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