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Simplifying 49.7(1.00 + -1x)(2.00 + -1x) = (2x) * 2 Multiply (1.00 + -1x) * (2.00 + -1x) 49.7(1.00(2.00 + -1x) + -1x * (2.00 + -1x)) = (2x) * 2 49.7((2.00 * 1.00 + -1x * 1.00) + -1x * (2.00 + -1x)) = (2x) * 2 49.7((2 + -1x) + -1x * (2.00 + -1x)) = (2x) * 2 49.7(2 + -1x + (2.00 * -1x + -1x * -1x)) = (2x) * 2 49.7(2 + -1x + (-2x + 1x2)) = (2x) * 2 Combine like terms: -1x + -2x = -3x 49.7(2 + -3x + 1x2) = (2x) * 2 (2 * 49.7 + -3x * 49.7 + 1x2 * 49.7) = (2x) * 2 (99.4 + -149.1x + 49.7x2) = (2x) * 2 Remove parenthesis around (2x) 99.4 + -149.1x + 49.7x2 = 2x * 2 Reorder the terms for easier multiplication: 99.4 + -149.1x + 49.7x2 = 2 * 2x Multiply 2 * 2 99.4 + -149.1x + 49.7x2 = 4x Solving 99.4 + -149.1x + 49.7x2 = 4x Solving for variable 'x'. Reorder the terms: 99.4 + -149.1x + -4x + 49.7x2 = 4x + -4x Combine like terms: -149.1x + -4x = -153.1x 99.4 + -153.1x + 49.7x2 = 4x + -4x Combine like terms: 4x + -4x = 0 99.4 + -153.1x + 49.7x2 = 0 Begin completing the square. Divide all terms by 49.7 the coefficient of the squared term: Divide each side by '49.7'. 2 + -3.080482897x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -3.080482897x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -3.080482897x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3.080482897x + x2 = 0 + -2 -3.080482897x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -3.080482897x + x2 = -2 The x term is -3.080482897x. Take half its coefficient (-1.540241449). Square it (2.372343721) and add it to both sides. Add '2.372343721' to each side of the equation. -3.080482897x + 2.372343721 + x2 = -2 + 2.372343721 Reorder the terms: 2.372343721 + -3.080482897x + x2 = -2 + 2.372343721 Combine like terms: -2 + 2.372343721 = 0.372343721 2.372343721 + -3.080482897x + x2 = 0.372343721 Factor a perfect square on the left side: (x + -1.540241449)(x + -1.540241449) = 0.372343721 Calculate the square root of the right side: 0.610199739 Break this problem into two subproblems by setting (x + -1.540241449) equal to 0.610199739 and -0.610199739.Subproblem 1
x + -1.540241449 = 0.610199739 Simplifying x + -1.540241449 = 0.610199739 Reorder the terms: -1.540241449 + x = 0.610199739 Solving -1.540241449 + x = 0.610199739 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.540241449' to each side of the equation. -1.540241449 + 1.540241449 + x = 0.610199739 + 1.540241449 Combine like terms: -1.540241449 + 1.540241449 = 0.000000000 0.000000000 + x = 0.610199739 + 1.540241449 x = 0.610199739 + 1.540241449 Combine like terms: 0.610199739 + 1.540241449 = 2.150441188 x = 2.150441188 Simplifying x = 2.150441188Subproblem 2
x + -1.540241449 = -0.610199739 Simplifying x + -1.540241449 = -0.610199739 Reorder the terms: -1.540241449 + x = -0.610199739 Solving -1.540241449 + x = -0.610199739 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.540241449' to each side of the equation. -1.540241449 + 1.540241449 + x = -0.610199739 + 1.540241449 Combine like terms: -1.540241449 + 1.540241449 = 0.000000000 0.000000000 + x = -0.610199739 + 1.540241449 x = -0.610199739 + 1.540241449 Combine like terms: -0.610199739 + 1.540241449 = 0.93004171 x = 0.93004171 Simplifying x = 0.93004171Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.150441188, 0.93004171}
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