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Simplifying 0.04x + 0.06x(10000 + -1x) = 480 0.04x + (10000 * 0.06x + -1x * 0.06x) = 480 0.04x + (600x + -0.06x2) = 480 Combine like terms: 0.04x + 600x = 600.04x 600.04x + -0.06x2 = 480 Solving 600.04x + -0.06x2 = 480 Solving for variable 'x'. Reorder the terms: -480 + 600.04x + -0.06x2 = 480 + -480 Combine like terms: 480 + -480 = 0 -480 + 600.04x + -0.06x2 = 0 Begin completing the square. Divide all terms by -0.06 the coefficient of the squared term: Divide each side by '-0.06'. 8000 + -10000.66667x + x2 = 0 Move the constant term to the right: Add '-8000' to each side of the equation. 8000 + -10000.66667x + -8000 + x2 = 0 + -8000 Reorder the terms: 8000 + -8000 + -10000.66667x + x2 = 0 + -8000 Combine like terms: 8000 + -8000 = 0 0 + -10000.66667x + x2 = 0 + -8000 -10000.66667x + x2 = 0 + -8000 Combine like terms: 0 + -8000 = -8000 -10000.66667x + x2 = -8000 The x term is -10000.66667x. Take half its coefficient (-5000.333335). Square it (25003333.46) and add it to both sides. Add '25003333.46' to each side of the equation. -10000.66667x + 25003333.46 + x2 = -8000 + 25003333.46 Reorder the terms: 25003333.46 + -10000.66667x + x2 = -8000 + 25003333.46 Combine like terms: -8000 + 25003333.46 = 24995333.46 25003333.46 + -10000.66667x + x2 = 24995333.46 Factor a perfect square on the left side: (x + -5000.333335)(x + -5000.333335) = 24995333.46 Calculate the square root of the right side: 4999.533324221 Break this problem into two subproblems by setting (x + -5000.333335) equal to 4999.533324221 and -4999.533324221.Subproblem 1
x + -5000.333335 = 4999.533324221 Simplifying x + -5000.333335 = 4999.533324221 Reorder the terms: -5000.333335 + x = 4999.533324221 Solving -5000.333335 + x = 4999.533324221 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5000.333335' to each side of the equation. -5000.333335 + 5000.333335 + x = 4999.533324221 + 5000.333335 Combine like terms: -5000.333335 + 5000.333335 = 0.000000 0.000000 + x = 4999.533324221 + 5000.333335 x = 4999.533324221 + 5000.333335 Combine like terms: 4999.533324221 + 5000.333335 = 9999.866659221 x = 9999.866659221 Simplifying x = 9999.866659221Subproblem 2
x + -5000.333335 = -4999.533324221 Simplifying x + -5000.333335 = -4999.533324221 Reorder the terms: -5000.333335 + x = -4999.533324221 Solving -5000.333335 + x = -4999.533324221 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5000.333335' to each side of the equation. -5000.333335 + 5000.333335 + x = -4999.533324221 + 5000.333335 Combine like terms: -5000.333335 + 5000.333335 = 0.000000 0.000000 + x = -4999.533324221 + 5000.333335 x = -4999.533324221 + 5000.333335 Combine like terms: -4999.533324221 + 5000.333335 = 0.800010779 x = 0.800010779 Simplifying x = 0.800010779Solution
The solution to the problem is based on the solutions from the subproblems. x = {9999.866659221, 0.800010779}
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