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Simplifying 0.002X(180 + -1X) = 6.4 (180 * 0.002X + -1X * 0.002X) = 6.4 (0.36X + -0.002X2) = 6.4 Solving 0.36X + -0.002X2 = 6.4 Solving for variable 'X'. Reorder the terms: -6.4 + 0.36X + -0.002X2 = 6.4 + -6.4 Combine like terms: 6.4 + -6.4 = 0.0 -6.4 + 0.36X + -0.002X2 = 0.0 Begin completing the square. Divide all terms by -0.002 the coefficient of the squared term: Divide each side by '-0.002'. 3200 + -180X + X2 = 0 Move the constant term to the right: Add '-3200' to each side of the equation. 3200 + -180X + -3200 + X2 = 0 + -3200 Reorder the terms: 3200 + -3200 + -180X + X2 = 0 + -3200 Combine like terms: 3200 + -3200 = 0 0 + -180X + X2 = 0 + -3200 -180X + X2 = 0 + -3200 Combine like terms: 0 + -3200 = -3200 -180X + X2 = -3200 The X term is -180X. Take half its coefficient (-90). Square it (8100) and add it to both sides. Add '8100' to each side of the equation. -180X + 8100 + X2 = -3200 + 8100 Reorder the terms: 8100 + -180X + X2 = -3200 + 8100 Combine like terms: -3200 + 8100 = 4900 8100 + -180X + X2 = 4900 Factor a perfect square on the left side: (X + -90)(X + -90) = 4900 Calculate the square root of the right side: 70 Break this problem into two subproblems by setting (X + -90) equal to 70 and -70.Subproblem 1
X + -90 = 70 Simplifying X + -90 = 70 Reorder the terms: -90 + X = 70 Solving -90 + X = 70 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '90' to each side of the equation. -90 + 90 + X = 70 + 90 Combine like terms: -90 + 90 = 0 0 + X = 70 + 90 X = 70 + 90 Combine like terms: 70 + 90 = 160 X = 160 Simplifying X = 160Subproblem 2
X + -90 = -70 Simplifying X + -90 = -70 Reorder the terms: -90 + X = -70 Solving -90 + X = -70 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '90' to each side of the equation. -90 + 90 + X = -70 + 90 Combine like terms: -90 + 90 = 0 0 + X = -70 + 90 X = -70 + 90 Combine like terms: -70 + 90 = 20 X = 20 Simplifying X = 20Solution
The solution to the problem is based on the solutions from the subproblems. X = {160, 20}
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