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Simplifying ((0.03 + -1x)(0.02 + -1x)) = 0 Multiply (0.03 + -1x) * (0.02 + -1x) ((0.03(0.02 + -1x) + -1x * (0.02 + -1x))) = 0 (((0.02 * 0.03 + -1x * 0.03) + -1x * (0.02 + -1x))) = 0 (((0.0006 + -0.03x) + -1x * (0.02 + -1x))) = 0 ((0.0006 + -0.03x + (0.02 * -1x + -1x * -1x))) = 0 ((0.0006 + -0.03x + (-0.02x + 1x2))) = 0 Combine like terms: -0.03x + -0.02x = -0.05x ((0.0006 + -0.05x + 1x2)) = 0 (0.0006 + -0.05x + 1x2) = 0 Remove parenthesis around (0.0006 + -0.05x + 1x2) 0.0006 + -0.05x + 1x2 = 0 Solving 0.0006 + -0.05x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.0006' to each side of the equation. 0.0006 + -0.05x + -0.0006 + x2 = 0 + -0.0006 Reorder the terms: 0.0006 + -0.0006 + -0.05x + x2 = 0 + -0.0006 Combine like terms: 0.0006 + -0.0006 = 0.0000 0.0000 + -0.05x + x2 = 0 + -0.0006 -0.05x + x2 = 0 + -0.0006 Combine like terms: 0 + -0.0006 = -0.0006 -0.05x + x2 = -0.0006 The x term is -0.05x. Take half its coefficient (-0.025). Square it (0.000625) and add it to both sides. Add '0.000625' to each side of the equation. -0.05x + 0.000625 + x2 = -0.0006 + 0.000625 Reorder the terms: 0.000625 + -0.05x + x2 = -0.0006 + 0.000625 Combine like terms: -0.0006 + 0.000625 = 0.000025 0.000625 + -0.05x + x2 = 0.000025 Factor a perfect square on the left side: (x + -0.025)(x + -0.025) = 0.000025 Calculate the square root of the right side: 0.005 Break this problem into two subproblems by setting (x + -0.025) equal to 0.005 and -0.005.Subproblem 1
x + -0.025 = 0.005 Simplifying x + -0.025 = 0.005 Reorder the terms: -0.025 + x = 0.005 Solving -0.025 + x = 0.005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.025' to each side of the equation. -0.025 + 0.025 + x = 0.005 + 0.025 Combine like terms: -0.025 + 0.025 = 0.000 0.000 + x = 0.005 + 0.025 x = 0.005 + 0.025 Combine like terms: 0.005 + 0.025 = 0.03 x = 0.03 Simplifying x = 0.03Subproblem 2
x + -0.025 = -0.005 Simplifying x + -0.025 = -0.005 Reorder the terms: -0.025 + x = -0.005 Solving -0.025 + x = -0.005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.025' to each side of the equation. -0.025 + 0.025 + x = -0.005 + 0.025 Combine like terms: -0.025 + 0.025 = 0.000 0.000 + x = -0.005 + 0.025 x = -0.005 + 0.025 Combine like terms: -0.005 + 0.025 = 0.02 x = 0.02 Simplifying x = 0.02Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.03, 0.02}
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