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Simplifying 18(0.05 + -1x)(0.10 + -1x) = 0 Multiply (0.05 + -1x) * (0.10 + -1x) 18(0.05(0.10 + -1x) + -1x * (0.10 + -1x)) = 0 18((0.10 * 0.05 + -1x * 0.05) + -1x * (0.10 + -1x)) = 0 18((0.005 + -0.05x) + -1x * (0.10 + -1x)) = 0 18(0.005 + -0.05x + (0.10 * -1x + -1x * -1x)) = 0 18(0.005 + -0.05x + (-0.1x + 1x2)) = 0 Combine like terms: -0.05x + -0.1x = -0.15x 18(0.005 + -0.15x + 1x2) = 0 (0.005 * 18 + -0.15x * 18 + 1x2 * 18) = 0 (0.09 + -2.7x + 18x2) = 0 Solving 0.09 + -2.7x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 0.005 + -0.15x + x2 = 0 Move the constant term to the right: Add '-0.005' to each side of the equation. 0.005 + -0.15x + -0.005 + x2 = 0 + -0.005 Reorder the terms: 0.005 + -0.005 + -0.15x + x2 = 0 + -0.005 Combine like terms: 0.005 + -0.005 = 0.000 0.000 + -0.15x + x2 = 0 + -0.005 -0.15x + x2 = 0 + -0.005 Combine like terms: 0 + -0.005 = -0.005 -0.15x + x2 = -0.005 The x term is -0.15x. Take half its coefficient (-0.075). Square it (0.005625) and add it to both sides. Add '0.005625' to each side of the equation. -0.15x + 0.005625 + x2 = -0.005 + 0.005625 Reorder the terms: 0.005625 + -0.15x + x2 = -0.005 + 0.005625 Combine like terms: -0.005 + 0.005625 = 0.000625 0.005625 + -0.15x + x2 = 0.000625 Factor a perfect square on the left side: (x + -0.075)(x + -0.075) = 0.000625 Calculate the square root of the right side: 0.025 Break this problem into two subproblems by setting (x + -0.075) equal to 0.025 and -0.025.Subproblem 1
x + -0.075 = 0.025 Simplifying x + -0.075 = 0.025 Reorder the terms: -0.075 + x = 0.025 Solving -0.075 + x = 0.025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.075' to each side of the equation. -0.075 + 0.075 + x = 0.025 + 0.075 Combine like terms: -0.075 + 0.075 = 0.000 0.000 + x = 0.025 + 0.075 x = 0.025 + 0.075 Combine like terms: 0.025 + 0.075 = 0.1 x = 0.1 Simplifying x = 0.1Subproblem 2
x + -0.075 = -0.025 Simplifying x + -0.075 = -0.025 Reorder the terms: -0.075 + x = -0.025 Solving -0.075 + x = -0.025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.075' to each side of the equation. -0.075 + 0.075 + x = -0.025 + 0.075 Combine like terms: -0.075 + 0.075 = 0.000 0.000 + x = -0.025 + 0.075 x = -0.025 + 0.075 Combine like terms: -0.025 + 0.075 = 0.05 x = 0.05 Simplifying x = 0.05Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1, 0.05}
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