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Simplifying 49.7(1.00 + -1x)(2.00 + -1x) = 2x2 Multiply (1.00 + -1x) * (2.00 + -1x) 49.7(1.00(2.00 + -1x) + -1x * (2.00 + -1x)) = 2x2 49.7((2.00 * 1.00 + -1x * 1.00) + -1x * (2.00 + -1x)) = 2x2 49.7((2 + -1x) + -1x * (2.00 + -1x)) = 2x2 49.7(2 + -1x + (2.00 * -1x + -1x * -1x)) = 2x2 49.7(2 + -1x + (-2x + 1x2)) = 2x2 Combine like terms: -1x + -2x = -3x 49.7(2 + -3x + 1x2) = 2x2 (2 * 49.7 + -3x * 49.7 + 1x2 * 49.7) = 2x2 (99.4 + -149.1x + 49.7x2) = 2x2 Solving 99.4 + -149.1x + 49.7x2 = 2x2 Solving for variable 'x'. Combine like terms: 49.7x2 + -2x2 = 47.7x2 99.4 + -149.1x + 47.7x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 99.4 + -149.1x + 47.7x2 = 0 Begin completing the square. Divide all terms by 47.7 the coefficient of the squared term: Divide each side by '47.7'. 2.083857442 + -3.125786164x + x2 = 0 Move the constant term to the right: Add '-2.083857442' to each side of the equation. 2.083857442 + -3.125786164x + -2.083857442 + x2 = 0 + -2.083857442 Reorder the terms: 2.083857442 + -2.083857442 + -3.125786164x + x2 = 0 + -2.083857442 Combine like terms: 2.083857442 + -2.083857442 = 0.000000000 0.000000000 + -3.125786164x + x2 = 0 + -2.083857442 -3.125786164x + x2 = 0 + -2.083857442 Combine like terms: 0 + -2.083857442 = -2.083857442 -3.125786164x + x2 = -2.083857442 The x term is -3.125786164x. Take half its coefficient (-1.562893082). Square it (2.442634786) and add it to both sides. Add '2.442634786' to each side of the equation. -3.125786164x + 2.442634786 + x2 = -2.083857442 + 2.442634786 Reorder the terms: 2.442634786 + -3.125786164x + x2 = -2.083857442 + 2.442634786 Combine like terms: -2.083857442 + 2.442634786 = 0.358777344 2.442634786 + -3.125786164x + x2 = 0.358777344 Factor a perfect square on the left side: (x + -1.562893082)(x + -1.562893082) = 0.358777344 Calculate the square root of the right side: 0.598980253 Break this problem into two subproblems by setting (x + -1.562893082) equal to 0.598980253 and -0.598980253.Subproblem 1
x + -1.562893082 = 0.598980253 Simplifying x + -1.562893082 = 0.598980253 Reorder the terms: -1.562893082 + x = 0.598980253 Solving -1.562893082 + x = 0.598980253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.562893082' to each side of the equation. -1.562893082 + 1.562893082 + x = 0.598980253 + 1.562893082 Combine like terms: -1.562893082 + 1.562893082 = 0.000000000 0.000000000 + x = 0.598980253 + 1.562893082 x = 0.598980253 + 1.562893082 Combine like terms: 0.598980253 + 1.562893082 = 2.161873335 x = 2.161873335 Simplifying x = 2.161873335Subproblem 2
x + -1.562893082 = -0.598980253 Simplifying x + -1.562893082 = -0.598980253 Reorder the terms: -1.562893082 + x = -0.598980253 Solving -1.562893082 + x = -0.598980253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.562893082' to each side of the equation. -1.562893082 + 1.562893082 + x = -0.598980253 + 1.562893082 Combine like terms: -1.562893082 + 1.562893082 = 0.000000000 0.000000000 + x = -0.598980253 + 1.562893082 x = -0.598980253 + 1.562893082 Combine like terms: -0.598980253 + 1.562893082 = 0.963912829 x = 0.963912829 Simplifying x = 0.963912829Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.161873335, 0.963912829}
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