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Simplifying (0.1 + x)(0.20 + x) = 0.00000000012 Multiply (0.1 + x) * (0.20 + x) (0.1(0.20 + x) + x(0.20 + x)) = 0.00000000012 ((0.20 * 0.1 + x * 0.1) + x(0.20 + x)) = 0.00000000012 ((0.02 + 0.1x) + x(0.20 + x)) = 0.00000000012 (0.02 + 0.1x + (0.20 * x + x * x)) = 0.00000000012 (0.02 + 0.1x + (0.20x + x2)) = 0.00000000012 Combine like terms: 0.1x + 0.20x = 0.3x (0.02 + 0.3x + x2) = 0.00000000012 Solving 0.02 + 0.3x + x2 = 0.00000000012 Solving for variable 'x'. Reorder the terms: 0.02 + -0.00000000012 + 0.3x + x2 = 0.00000000012 + -0.00000000012 Combine like terms: 0.02 + -0.00000000012 = 0.01999999988 0.01999999988 + 0.3x + x2 = 0.00000000012 + -0.00000000012 Combine like terms: 0.00000000012 + -0.00000000012 = 0.00000000000 0.01999999988 + 0.3x + x2 = 0.00000000000 Begin completing the square. Move the constant term to the right: Add '-0.01999999988' to each side of the equation. 0.01999999988 + 0.3x + -0.01999999988 + x2 = 0.00000000000 + -0.01999999988 Reorder the terms: 0.01999999988 + -0.01999999988 + 0.3x + x2 = 0.00000000000 + -0.01999999988 Combine like terms: 0.01999999988 + -0.01999999988 = 0.00000000000 0.00000000000 + 0.3x + x2 = 0.00000000000 + -0.01999999988 0.3x + x2 = 0.00000000000 + -0.01999999988 Combine like terms: 0.00000000000 + -0.01999999988 = -0.01999999988 0.3x + x2 = -0.01999999988 The x term is 0.3x. Take half its coefficient (0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. 0.3x + 0.0225 + x2 = -0.01999999988 + 0.0225 Reorder the terms: 0.0225 + 0.3x + x2 = -0.01999999988 + 0.0225 Combine like terms: -0.01999999988 + 0.0225 = 0.00250000012 0.0225 + 0.3x + x2 = 0.00250000012 Factor a perfect square on the left side: (x + 0.15)(x + 0.15) = 0.00250000012 Calculate the square root of the right side: 0.050000001 Break this problem into two subproblems by setting (x + 0.15) equal to 0.050000001 and -0.050000001.Subproblem 1
x + 0.15 = 0.050000001 Simplifying x + 0.15 = 0.050000001 Reorder the terms: 0.15 + x = 0.050000001 Solving 0.15 + x = 0.050000001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = 0.050000001 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = 0.050000001 + -0.15 x = 0.050000001 + -0.15 Combine like terms: 0.050000001 + -0.15 = -0.099999999 x = -0.099999999 Simplifying x = -0.099999999Subproblem 2
x + 0.15 = -0.050000001 Simplifying x + 0.15 = -0.050000001 Reorder the terms: 0.15 + x = -0.050000001 Solving 0.15 + x = -0.050000001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = -0.050000001 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = -0.050000001 + -0.15 x = -0.050000001 + -0.15 Combine like terms: -0.050000001 + -0.15 = -0.200000001 x = -0.200000001 Simplifying x = -0.200000001Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.099999999, -0.200000001}
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