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Simplifying (12 + -0.4x)(2 + -0.1x) = 0 Multiply (12 + -0.4x) * (2 + -0.1x) (12(2 + -0.1x) + -0.4x * (2 + -0.1x)) = 0 ((2 * 12 + -0.1x * 12) + -0.4x * (2 + -0.1x)) = 0 ((24 + -1.2x) + -0.4x * (2 + -0.1x)) = 0 (24 + -1.2x + (2 * -0.4x + -0.1x * -0.4x)) = 0 (24 + -1.2x + (-0.8x + 0.04x2)) = 0 Combine like terms: -1.2x + -0.8x = -2x (24 + -2x + 0.04x2) = 0 Solving 24 + -2x + 0.04x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.04 the coefficient of the squared term: Divide each side by '0.04'. 600 + -50x + x2 = 0 Move the constant term to the right: Add '-600' to each side of the equation. 600 + -50x + -600 + x2 = 0 + -600 Reorder the terms: 600 + -600 + -50x + x2 = 0 + -600 Combine like terms: 600 + -600 = 0 0 + -50x + x2 = 0 + -600 -50x + x2 = 0 + -600 Combine like terms: 0 + -600 = -600 -50x + x2 = -600 The x term is -50x. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50x + 625 + x2 = -600 + 625 Reorder the terms: 625 + -50x + x2 = -600 + 625 Combine like terms: -600 + 625 = 25 625 + -50x + x2 = 25 Factor a perfect square on the left side: (x + -25)(x + -25) = 25 Calculate the square root of the right side: 5 Break this problem into two subproblems by setting (x + -25) equal to 5 and -5.Subproblem 1
x + -25 = 5 Simplifying x + -25 = 5 Reorder the terms: -25 + x = 5 Solving -25 + x = 5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = 5 + 25 Combine like terms: -25 + 25 = 0 0 + x = 5 + 25 x = 5 + 25 Combine like terms: 5 + 25 = 30 x = 30 Simplifying x = 30Subproblem 2
x + -25 = -5 Simplifying x + -25 = -5 Reorder the terms: -25 + x = -5 Solving -25 + x = -5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = -5 + 25 Combine like terms: -25 + 25 = 0 0 + x = -5 + 25 x = -5 + 25 Combine like terms: -5 + 25 = 20 x = 20 Simplifying x = 20Solution
The solution to the problem is based on the solutions from the subproblems. x = {30, 20}
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