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Simplifying (0.1 + -1x)(0.2 + -1x) = 1 Multiply (0.1 + -1x) * (0.2 + -1x) (0.1(0.2 + -1x) + -1x * (0.2 + -1x)) = 1 ((0.2 * 0.1 + -1x * 0.1) + -1x * (0.2 + -1x)) = 1 ((0.02 + -0.1x) + -1x * (0.2 + -1x)) = 1 (0.02 + -0.1x + (0.2 * -1x + -1x * -1x)) = 1 (0.02 + -0.1x + (-0.2x + 1x2)) = 1 Combine like terms: -0.1x + -0.2x = -0.3x (0.02 + -0.3x + 1x2) = 1 Solving 0.02 + -0.3x + 1x2 = 1 Solving for variable 'x'. Reorder the terms: 0.02 + -1 + -0.3x + 1x2 = 1 + -1 Combine like terms: 0.02 + -1 = -0.98 -0.98 + -0.3x + 1x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -0.98 + -0.3x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '0.98' to each side of the equation. -0.98 + -0.3x + 0.98 + x2 = 0 + 0.98 Reorder the terms: -0.98 + 0.98 + -0.3x + x2 = 0 + 0.98 Combine like terms: -0.98 + 0.98 = 0.00 0.00 + -0.3x + x2 = 0 + 0.98 -0.3x + x2 = 0 + 0.98 Combine like terms: 0 + 0.98 = 0.98 -0.3x + x2 = 0.98 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 = 0.98 + 0.0225 Reorder the terms: 0.0225 + -0.3x + x2 = 0.98 + 0.0225 Combine like terms: 0.98 + 0.0225 = 1.0025 0.0225 + -0.3x + x2 = 1.0025 Factor a perfect square on the left side: (x + -0.15)(x + -0.15) = 1.0025 Calculate the square root of the right side: 1.00124922 Break this problem into two subproblems by setting (x + -0.15) equal to 1.00124922 and -1.00124922.Subproblem 1
x + -0.15 = 1.00124922 Simplifying x + -0.15 = 1.00124922 Reorder the terms: -0.15 + x = 1.00124922 Solving -0.15 + x = 1.00124922 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 = 1.00124922 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = 1.00124922 + 0.15 x = 1.00124922 + 0.15 Combine like terms: 1.00124922 + 0.15 = 1.15124922 x = 1.15124922 Simplifying x = 1.15124922Subproblem 2
x + -0.15 = -1.00124922 Simplifying x + -0.15 = -1.00124922 Reorder the terms: -0.15 + x = -1.00124922 Solving -0.15 + x = -1.00124922 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 = -1.00124922 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = -1.00124922 + 0.15 x = -1.00124922 + 0.15 Combine like terms: -1.00124922 + 0.15 = -0.85124922 x = -0.85124922 Simplifying x = -0.85124922Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.15124922, -0.85124922}
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