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Simplifying (1.00 + -1x)(0.07 + -1x) = 0.10 Multiply (1.00 + -1x) * (0.07 + -1x) (1.00(0.07 + -1x) + -1x * (0.07 + -1x)) = 0.10 ((0.07 * 1.00 + -1x * 1.00) + -1x * (0.07 + -1x)) = 0.10 ((0.07 + -1x) + -1x * (0.07 + -1x)) = 0.10 (0.07 + -1x + (0.07 * -1x + -1x * -1x)) = 0.10 (0.07 + -1x + (-0.07x + 1x2)) = 0.10 Combine like terms: -1x + -0.07x = -1.07x (0.07 + -1.07x + 1x2) = 0.10 Solving 0.07 + -1.07x + 1x2 = 0.10 Solving for variable 'x'. Reorder the terms: 0.07 + -0.10 + -1.07x + 1x2 = 0.10 + -0.10 Combine like terms: 0.07 + -0.10 = -0.03 -0.03 + -1.07x + 1x2 = 0.10 + -0.10 Combine like terms: 0.10 + -0.10 = 0.00 -0.03 + -1.07x + 1x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '0.03' to each side of the equation. -0.03 + -1.07x + 0.03 + x2 = 0.00 + 0.03 Reorder the terms: -0.03 + 0.03 + -1.07x + x2 = 0.00 + 0.03 Combine like terms: -0.03 + 0.03 = 0.00 0.00 + -1.07x + x2 = 0.00 + 0.03 -1.07x + x2 = 0.00 + 0.03 Combine like terms: 0.00 + 0.03 = 0.03 -1.07x + x2 = 0.03 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 = 0.03 + 0.286225 Reorder the terms: 0.286225 + -1.07x + x2 = 0.03 + 0.286225 Combine like terms: 0.03 + 0.286225 = 0.316225 0.286225 + -1.07x + x2 = 0.316225 Factor a perfect square on the left side: (x + -0.535)(x + -0.535) = 0.316225 Calculate the square root of the right side: 0.562338866 Break this problem into two subproblems by setting (x + -0.535) equal to 0.562338866 and -0.562338866.Subproblem 1
x + -0.535 = 0.562338866 Simplifying x + -0.535 = 0.562338866 Reorder the terms: -0.535 + x = 0.562338866 Solving -0.535 + x = 0.562338866 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 = 0.562338866 + 0.535 Combine like terms: -0.535 + 0.535 = 0.000 0.000 + x = 0.562338866 + 0.535 x = 0.562338866 + 0.535 Combine like terms: 0.562338866 + 0.535 = 1.097338866 x = 1.097338866 Simplifying x = 1.097338866Subproblem 2
x + -0.535 = -0.562338866 Simplifying x + -0.535 = -0.562338866 Reorder the terms: -0.535 + x = -0.562338866 Solving -0.535 + x = -0.562338866 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 = -0.562338866 + 0.535 Combine like terms: -0.535 + 0.535 = 0.000 0.000 + x = -0.562338866 + 0.535 x = -0.562338866 + 0.535 Combine like terms: -0.562338866 + 0.535 = -0.027338866 x = -0.027338866 Simplifying x = -0.027338866Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.097338866, -0.027338866}
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