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Simplifying 0 = (10 + -0.05X)(60 + X) Multiply (10 + -0.05X) * (60 + X) 0 = (10(60 + X) + -0.05X * (60 + X)) 0 = ((60 * 10 + X * 10) + -0.05X * (60 + X)) 0 = ((600 + 10X) + -0.05X * (60 + X)) 0 = (600 + 10X + (60 * -0.05X + X * -0.05X)) 0 = (600 + 10X + (-3X + -0.05X2)) Combine like terms: 10X + -3X = 7X 0 = (600 + 7X + -0.05X2) Solving 0 = 600 + 7X + -0.05X2 Solving for variable 'X'. Combine like terms: 0 + -600 = -600 -600 + -7X + 0.05X2 = 600 + 7X + -0.05X2 + -600 + -7X + 0.05X2 Reorder the terms: -600 + -7X + 0.05X2 = 600 + -600 + 7X + -7X + -0.05X2 + 0.05X2 Combine like terms: 600 + -600 = 0 -600 + -7X + 0.05X2 = 0 + 7X + -7X + -0.05X2 + 0.05X2 -600 + -7X + 0.05X2 = 7X + -7X + -0.05X2 + 0.05X2 Combine like terms: 7X + -7X = 0 -600 + -7X + 0.05X2 = 0 + -0.05X2 + 0.05X2 -600 + -7X + 0.05X2 = -0.05X2 + 0.05X2 Combine like terms: -0.05X2 + 0.05X2 = 0.00 -600 + -7X + 0.05X2 = 0.00 Begin completing the square. Divide all terms by 0.05 the coefficient of the squared term: Divide each side by '0.05'. -12000 + -140X + X2 = 0 Move the constant term to the right: Add '12000' to each side of the equation. -12000 + -140X + 12000 + X2 = 0 + 12000 Reorder the terms: -12000 + 12000 + -140X + X2 = 0 + 12000 Combine like terms: -12000 + 12000 = 0 0 + -140X + X2 = 0 + 12000 -140X + X2 = 0 + 12000 Combine like terms: 0 + 12000 = 12000 -140X + X2 = 12000 The X term is -140X. Take half its coefficient (-70). Square it (4900) and add it to both sides. Add '4900' to each side of the equation. -140X + 4900 + X2 = 12000 + 4900 Reorder the terms: 4900 + -140X + X2 = 12000 + 4900 Combine like terms: 12000 + 4900 = 16900 4900 + -140X + X2 = 16900 Factor a perfect square on the left side: (X + -70)(X + -70) = 16900 Calculate the square root of the right side: 130 Break this problem into two subproblems by setting (X + -70) equal to 130 and -130.Subproblem 1
X + -70 = 130 Simplifying X + -70 = 130 Reorder the terms: -70 + X = 130 Solving -70 + X = 130 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '70' to each side of the equation. -70 + 70 + X = 130 + 70 Combine like terms: -70 + 70 = 0 0 + X = 130 + 70 X = 130 + 70 Combine like terms: 130 + 70 = 200 X = 200 Simplifying X = 200Subproblem 2
X + -70 = -130 Simplifying X + -70 = -130 Reorder the terms: -70 + X = -130 Solving -70 + X = -130 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '70' to each side of the equation. -70 + 70 + X = -130 + 70 Combine like terms: -70 + 70 = 0 0 + X = -130 + 70 X = -130 + 70 Combine like terms: -130 + 70 = -60 X = -60 Simplifying X = -60Solution
The solution to the problem is based on the solutions from the subproblems. X = {200, -60}
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