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Simplifying (8 + -0.2X)(6 + -0.1X) = 0 Multiply (8 + -0.2X) * (6 + -0.1X) (8(6 + -0.1X) + -0.2X * (6 + -0.1X)) = 0 ((6 * 8 + -0.1X * 8) + -0.2X * (6 + -0.1X)) = 0 ((48 + -0.8X) + -0.2X * (6 + -0.1X)) = 0 (48 + -0.8X + (6 * -0.2X + -0.1X * -0.2X)) = 0 (48 + -0.8X + (-1.2X + 0.02X2)) = 0 Combine like terms: -0.8X + -1.2X = -2X (48 + -2X + 0.02X2) = 0 Solving 48 + -2X + 0.02X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 0.02 the coefficient of the squared term: Divide each side by '0.02'. 2400 + -100X + X2 = 0 Move the constant term to the right: Add '-2400' to each side of the equation. 2400 + -100X + -2400 + X2 = 0 + -2400 Reorder the terms: 2400 + -2400 + -100X + X2 = 0 + -2400 Combine like terms: 2400 + -2400 = 0 0 + -100X + X2 = 0 + -2400 -100X + X2 = 0 + -2400 Combine like terms: 0 + -2400 = -2400 -100X + X2 = -2400 The X term is -100X. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100X + 2500 + X2 = -2400 + 2500 Reorder the terms: 2500 + -100X + X2 = -2400 + 2500 Combine like terms: -2400 + 2500 = 100 2500 + -100X + X2 = 100 Factor a perfect square on the left side: (X + -50)(X + -50) = 100 Calculate the square root of the right side: 10 Break this problem into two subproblems by setting (X + -50) equal to 10 and -10.Subproblem 1
X + -50 = 10 Simplifying X + -50 = 10 Reorder the terms: -50 + X = 10 Solving -50 + X = 10 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + X = 10 + 50 Combine like terms: -50 + 50 = 0 0 + X = 10 + 50 X = 10 + 50 Combine like terms: 10 + 50 = 60 X = 60 Simplifying X = 60Subproblem 2
X + -50 = -10 Simplifying X + -50 = -10 Reorder the terms: -50 + X = -10 Solving -50 + X = -10 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + X = -10 + 50 Combine like terms: -50 + 50 = 0 0 + X = -10 + 50 X = -10 + 50 Combine like terms: -10 + 50 = 40 X = 40 Simplifying X = 40Solution
The solution to the problem is based on the solutions from the subproblems. X = {60, 40}
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