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Simplifying (1.00 + -1x)(0.07 + -1x)(0.10) = 0 Reorder the terms for easier multiplication: 0.10(1.00 + -1x)(0.07 + -1x) = 0 Multiply (1.00 + -1x) * (0.07 + -1x) 0.10(1.00(0.07 + -1x) + -1x * (0.07 + -1x)) = 0 0.10((0.07 * 1.00 + -1x * 1.00) + -1x * (0.07 + -1x)) = 0 0.10((0.07 + -1x) + -1x * (0.07 + -1x)) = 0 0.10(0.07 + -1x + (0.07 * -1x + -1x * -1x)) = 0 0.10(0.07 + -1x + (-0.07x + 1x2)) = 0 Combine like terms: -1x + -0.07x = -1.07x 0.10(0.07 + -1.07x + 1x2) = 0 (0.07 * 0.10 + -1.07x * 0.10 + 1x2 * 0.10) = 0 (0.007 + -0.107x + 0.1x2) = 0 Solving 0.007 + -0.107x + 0.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. 0.07 + -1.07x + x2 = 0 Move the constant term to the right: Add '-0.07' to each side of the equation. 0.07 + -1.07x + -0.07 + x2 = 0 + -0.07 Reorder the terms: 0.07 + -0.07 + -1.07x + x2 = 0 + -0.07 Combine like terms: 0.07 + -0.07 = 0.00 0.00 + -1.07x + x2 = 0 + -0.07 -1.07x + x2 = 0 + -0.07 Combine like terms: 0 + -0.07 = -0.07 -1.07x + x2 = -0.07 The x term is -1.07x. Take half its coefficient (-0.535). Square it (0.286225) and add it to both sides. Add '0.286225' to each side of the equation. -1.07x + 0.286225 + x2 = -0.07 + 0.286225 Reorder the terms: 0.286225 + -1.07x + x2 = -0.07 + 0.286225 Combine like terms: -0.07 + 0.286225 = 0.216225 0.286225 + -1.07x + x2 = 0.216225 Factor a perfect square on the left side: (x + -0.535)(x + -0.535) = 0.216225 Calculate the square root of the right side: 0.465 Break this problem into two subproblems by setting (x + -0.535) equal to 0.465 and -0.465.Subproblem 1
x + -0.535 = 0.465 Simplifying x + -0.535 = 0.465 Reorder the terms: -0.535 + x = 0.465 Solving -0.535 + x = 0.465 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.535' to each side of the equation. -0.535 + 0.535 + x = 0.465 + 0.535 Combine like terms: -0.535 + 0.535 = 0.000 0.000 + x = 0.465 + 0.535 x = 0.465 + 0.535 Combine like terms: 0.465 + 0.535 = 1 x = 1 Simplifying x = 1Subproblem 2
x + -0.535 = -0.465 Simplifying x + -0.535 = -0.465 Reorder the terms: -0.535 + x = -0.465 Solving -0.535 + x = -0.465 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.535' to each side of the equation. -0.535 + 0.535 + x = -0.465 + 0.535 Combine like terms: -0.535 + 0.535 = 0.000 0.000 + x = -0.465 + 0.535 x = -0.465 + 0.535 Combine like terms: -0.465 + 0.535 = 0.07 x = 0.07 Simplifying x = 0.07Solution
The solution to the problem is based on the solutions from the subproblems. x = {1, 0.07}
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