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Simplifying 550 = 50x + -0.01x2 Solving 550 = 50x + -0.01x2 Solving for variable 'x'. Reorder the terms: 550 + -50x + 0.01x2 = 50x + -50x + -0.01x2 + 0.01x2 Combine like terms: 50x + -50x = 0 550 + -50x + 0.01x2 = 0 + -0.01x2 + 0.01x2 550 + -50x + 0.01x2 = -0.01x2 + 0.01x2 Combine like terms: -0.01x2 + 0.01x2 = 0.00 550 + -50x + 0.01x2 = 0.00 Begin completing the square. Divide all terms by 0.01 the coefficient of the squared term: Divide each side by '0.01'. 55000 + -5000x + x2 = 0 Move the constant term to the right: Add '-55000' to each side of the equation. 55000 + -5000x + -55000 + x2 = 0 + -55000 Reorder the terms: 55000 + -55000 + -5000x + x2 = 0 + -55000 Combine like terms: 55000 + -55000 = 0 0 + -5000x + x2 = 0 + -55000 -5000x + x2 = 0 + -55000 Combine like terms: 0 + -55000 = -55000 -5000x + x2 = -55000 The x term is -5000x. Take half its coefficient (-2500). Square it (6250000) and add it to both sides. Add '6250000' to each side of the equation. -5000x + 6250000 + x2 = -55000 + 6250000 Reorder the terms: 6250000 + -5000x + x2 = -55000 + 6250000 Combine like terms: -55000 + 6250000 = 6195000 6250000 + -5000x + x2 = 6195000 Factor a perfect square on the left side: (x + -2500)(x + -2500) = 6195000 Calculate the square root of the right side: 2488.975692931 Break this problem into two subproblems by setting (x + -2500) equal to 2488.975692931 and -2488.975692931.Subproblem 1
x + -2500 = 2488.975692931 Simplifying x + -2500 = 2488.975692931 Reorder the terms: -2500 + x = 2488.975692931 Solving -2500 + x = 2488.975692931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2500' to each side of the equation. -2500 + 2500 + x = 2488.975692931 + 2500 Combine like terms: -2500 + 2500 = 0 0 + x = 2488.975692931 + 2500 x = 2488.975692931 + 2500 Combine like terms: 2488.975692931 + 2500 = 4988.975692931 x = 4988.975692931 Simplifying x = 4988.975692931Subproblem 2
x + -2500 = -2488.975692931 Simplifying x + -2500 = -2488.975692931 Reorder the terms: -2500 + x = -2488.975692931 Solving -2500 + x = -2488.975692931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2500' to each side of the equation. -2500 + 2500 + x = -2488.975692931 + 2500 Combine like terms: -2500 + 2500 = 0 0 + x = -2488.975692931 + 2500 x = -2488.975692931 + 2500 Combine like terms: -2488.975692931 + 2500 = 11.024307069 x = 11.024307069 Simplifying x = 11.024307069Solution
The solution to the problem is based on the solutions from the subproblems. x = {4988.975692931, 11.024307069}
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