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Simplifying 0.2x + 0.8x(50 + -1x) = 0.68(50) 0.2x + (50 * 0.8x + -1x * 0.8x) = 0.68(50) 0.2x + (40x + -0.8x2) = 0.68(50) Combine like terms: 0.2x + 40x = 40.2x 40.2x + -0.8x2 = 0.68(50) Multiply 0.68 * 50 40.2x + -0.8x2 = 34 Solving 40.2x + -0.8x2 = 34 Solving for variable 'x'. Reorder the terms: -34 + 40.2x + -0.8x2 = 34 + -34 Combine like terms: 34 + -34 = 0 -34 + 40.2x + -0.8x2 = 0 Begin completing the square. Divide all terms by -0.8 the coefficient of the squared term: Divide each side by '-0.8'. 42.5 + -50.25x + x2 = 0 Move the constant term to the right: Add '-42.5' to each side of the equation. 42.5 + -50.25x + -42.5 + x2 = 0 + -42.5 Reorder the terms: 42.5 + -42.5 + -50.25x + x2 = 0 + -42.5 Combine like terms: 42.5 + -42.5 = 0.0 0.0 + -50.25x + x2 = 0 + -42.5 -50.25x + x2 = 0 + -42.5 Combine like terms: 0 + -42.5 = -42.5 -50.25x + x2 = -42.5 The x term is -50.25x. Take half its coefficient (-25.125). Square it (631.265625) and add it to both sides. Add '631.265625' to each side of the equation. -50.25x + 631.265625 + x2 = -42.5 + 631.265625 Reorder the terms: 631.265625 + -50.25x + x2 = -42.5 + 631.265625 Combine like terms: -42.5 + 631.265625 = 588.765625 631.265625 + -50.25x + x2 = 588.765625 Factor a perfect square on the left side: (x + -25.125)(x + -25.125) = 588.765625 Calculate the square root of the right side: 24.264493092 Break this problem into two subproblems by setting (x + -25.125) equal to 24.264493092 and -24.264493092.Subproblem 1
x + -25.125 = 24.264493092 Simplifying x + -25.125 = 24.264493092 Reorder the terms: -25.125 + x = 24.264493092 Solving -25.125 + x = 24.264493092 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25.125' to each side of the equation. -25.125 + 25.125 + x = 24.264493092 + 25.125 Combine like terms: -25.125 + 25.125 = 0.000 0.000 + x = 24.264493092 + 25.125 x = 24.264493092 + 25.125 Combine like terms: 24.264493092 + 25.125 = 49.389493092 x = 49.389493092 Simplifying x = 49.389493092Subproblem 2
x + -25.125 = -24.264493092 Simplifying x + -25.125 = -24.264493092 Reorder the terms: -25.125 + x = -24.264493092 Solving -25.125 + x = -24.264493092 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25.125' to each side of the equation. -25.125 + 25.125 + x = -24.264493092 + 25.125 Combine like terms: -25.125 + 25.125 = 0.000 0.000 + x = -24.264493092 + 25.125 x = -24.264493092 + 25.125 Combine like terms: -24.264493092 + 25.125 = 0.860506908 x = 0.860506908 Simplifying x = 0.860506908Solution
The solution to the problem is based on the solutions from the subproblems. x = {49.389493092, 0.860506908}
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