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Simplifying 0.04 + 0.06x(10000 + -1x) = 480 0.04 + (10000 * 0.06x + -1x * 0.06x) = 480 0.04 + (600x + -0.06x2) = 480 Solving 0.04 + 600x + -0.06x2 = 480 Solving for variable 'x'. Reorder the terms: 0.04 + -480 + 600x + -0.06x2 = 480 + -480 Combine like terms: 0.04 + -480 = -479.96 -479.96 + 600x + -0.06x2 = 480 + -480 Combine like terms: 480 + -480 = 0 -479.96 + 600x + -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'. 7999.333333 + -10000x + x2 = 0 Move the constant term to the right: Add '-7999.333333' to each side of the equation. 7999.333333 + -10000x + -7999.333333 + x2 = 0 + -7999.333333 Reorder the terms: 7999.333333 + -7999.333333 + -10000x + x2 = 0 + -7999.333333 Combine like terms: 7999.333333 + -7999.333333 = 0.000000 0.000000 + -10000x + x2 = 0 + -7999.333333 -10000x + x2 = 0 + -7999.333333 Combine like terms: 0 + -7999.333333 = -7999.333333 -10000x + x2 = -7999.333333 The x term is -10000x. Take half its coefficient (-5000). Square it (25000000) and add it to both sides. Add '25000000' to each side of the equation. -10000x + 25000000 + x2 = -7999.333333 + 25000000 Reorder the terms: 25000000 + -10000x + x2 = -7999.333333 + 25000000 Combine like terms: -7999.333333 + 25000000 = 24992000.666667 25000000 + -10000x + x2 = 24992000.666667 Factor a perfect square on the left side: (x + -5000)(x + -5000) = 24992000.666667 Calculate the square root of the right side: 4999.200002667 Break this problem into two subproblems by setting (x + -5000) equal to 4999.200002667 and -4999.200002667.Subproblem 1
x + -5000 = 4999.200002667 Simplifying x + -5000 = 4999.200002667 Reorder the terms: -5000 + x = 4999.200002667 Solving -5000 + x = 4999.200002667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5000' to each side of the equation. -5000 + 5000 + x = 4999.200002667 + 5000 Combine like terms: -5000 + 5000 = 0 0 + x = 4999.200002667 + 5000 x = 4999.200002667 + 5000 Combine like terms: 4999.200002667 + 5000 = 9999.200002667 x = 9999.200002667 Simplifying x = 9999.200002667Subproblem 2
x + -5000 = -4999.200002667 Simplifying x + -5000 = -4999.200002667 Reorder the terms: -5000 + x = -4999.200002667 Solving -5000 + x = -4999.200002667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5000' to each side of the equation. -5000 + 5000 + x = -4999.200002667 + 5000 Combine like terms: -5000 + 5000 = 0 0 + x = -4999.200002667 + 5000 x = -4999.200002667 + 5000 Combine like terms: -4999.200002667 + 5000 = 0.799997333 x = 0.799997333 Simplifying x = 0.799997333Solution
The solution to the problem is based on the solutions from the subproblems. x = {9999.200002667, 0.799997333}
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