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Simplifying (1200 + 40X)(0.40 + -0.01X) = 0 Multiply (1200 + 40X) * (0.40 + -0.01X) (1200(0.40 + -0.01X) + 40X * (0.40 + -0.01X)) = 0 ((0.40 * 1200 + -0.01X * 1200) + 40X * (0.40 + -0.01X)) = 0 ((480 + -12X) + 40X * (0.40 + -0.01X)) = 0 (480 + -12X + (0.40 * 40X + -0.01X * 40X)) = 0 (480 + -12X + (16X + -0.4X2)) = 0 Combine like terms: -12X + 16X = 4X (480 + 4X + -0.4X2) = 0 Solving 480 + 4X + -0.4X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by -0.4 the coefficient of the squared term: Divide each side by '-0.4'. -1200 + -10X + X2 = 0 Move the constant term to the right: Add '1200' to each side of the equation. -1200 + -10X + 1200 + X2 = 0 + 1200 Reorder the terms: -1200 + 1200 + -10X + X2 = 0 + 1200 Combine like terms: -1200 + 1200 = 0 0 + -10X + X2 = 0 + 1200 -10X + X2 = 0 + 1200 Combine like terms: 0 + 1200 = 1200 -10X + X2 = 1200 The X term is -10X. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10X + 25 + X2 = 1200 + 25 Reorder the terms: 25 + -10X + X2 = 1200 + 25 Combine like terms: 1200 + 25 = 1225 25 + -10X + X2 = 1225 Factor a perfect square on the left side: (X + -5)(X + -5) = 1225 Calculate the square root of the right side: 35 Break this problem into two subproblems by setting (X + -5) equal to 35 and -35.Subproblem 1
X + -5 = 35 Simplifying X + -5 = 35 Reorder the terms: -5 + X = 35 Solving -5 + X = 35 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + X = 35 + 5 Combine like terms: -5 + 5 = 0 0 + X = 35 + 5 X = 35 + 5 Combine like terms: 35 + 5 = 40 X = 40 Simplifying X = 40Subproblem 2
X + -5 = -35 Simplifying X + -5 = -35 Reorder the terms: -5 + X = -35 Solving -5 + X = -35 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + X = -35 + 5 Combine like terms: -5 + 5 = 0 0 + X = -35 + 5 X = -35 + 5 Combine like terms: -35 + 5 = -30 X = -30 Simplifying X = -30Solution
The solution to the problem is based on the solutions from the subproblems. X = {40, -30}
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