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Simplifying 0.0175x + 0.02x(50000 + -1x) = 900 0.0175x + (50000 * 0.02x + -1x * 0.02x) = 900 0.0175x + (1000x + -0.02x2) = 900 Combine like terms: 0.0175x + 1000x = 1000.0175x 1000.0175x + -0.02x2 = 900 Solving 1000.0175x + -0.02x2 = 900 Solving for variable 'x'. Reorder the terms: -900 + 1000.0175x + -0.02x2 = 900 + -900 Combine like terms: 900 + -900 = 0 -900 + 1000.0175x + -0.02x2 = 0 Begin completing the square. Divide all terms by -0.02 the coefficient of the squared term: Divide each side by '-0.02'. 45000 + -50000.875x + x2 = 0 Move the constant term to the right: Add '-45000' to each side of the equation. 45000 + -50000.875x + -45000 + x2 = 0 + -45000 Reorder the terms: 45000 + -45000 + -50000.875x + x2 = 0 + -45000 Combine like terms: 45000 + -45000 = 0 0 + -50000.875x + x2 = 0 + -45000 -50000.875x + x2 = 0 + -45000 Combine like terms: 0 + -45000 = -45000 -50000.875x + x2 = -45000 The x term is -50000.875x. Take half its coefficient (-25000.4375). Square it (625021875.2) and add it to both sides. Add '625021875.2' to each side of the equation. -50000.875x + 625021875.2 + x2 = -45000 + 625021875.2 Reorder the terms: 625021875.2 + -50000.875x + x2 = -45000 + 625021875.2 Combine like terms: -45000 + 625021875.2 = 624976875.2 625021875.2 + -50000.875x + x2 = 624976875.2 Factor a perfect square on the left side: (x + -25000.4375)(x + -25000.4375) = 624976875.2 Calculate the square root of the right side: 24999.537499722 Break this problem into two subproblems by setting (x + -25000.4375) equal to 24999.537499722 and -24999.537499722.Subproblem 1
x + -25000.4375 = 24999.537499722 Simplifying x + -25000.4375 = 24999.537499722 Reorder the terms: -25000.4375 + x = 24999.537499722 Solving -25000.4375 + x = 24999.537499722 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25000.4375' to each side of the equation. -25000.4375 + 25000.4375 + x = 24999.537499722 + 25000.4375 Combine like terms: -25000.4375 + 25000.4375 = 0.0000 0.0000 + x = 24999.537499722 + 25000.4375 x = 24999.537499722 + 25000.4375 Combine like terms: 24999.537499722 + 25000.4375 = 49999.974999722 x = 49999.974999722 Simplifying x = 49999.974999722Subproblem 2
x + -25000.4375 = -24999.537499722 Simplifying x + -25000.4375 = -24999.537499722 Reorder the terms: -25000.4375 + x = -24999.537499722 Solving -25000.4375 + x = -24999.537499722 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25000.4375' to each side of the equation. -25000.4375 + 25000.4375 + x = -24999.537499722 + 25000.4375 Combine like terms: -25000.4375 + 25000.4375 = 0.0000 0.0000 + x = -24999.537499722 + 25000.4375 x = -24999.537499722 + 25000.4375 Combine like terms: -24999.537499722 + 25000.4375 = 0.900000278 x = 0.900000278 Simplifying x = 0.900000278Solution
The solution to the problem is based on the solutions from the subproblems. x = {49999.974999722, 0.900000278}
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