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Simplifying 299 = 200 + 6x + 0.01x2 Solving 299 = 200 + 6x + 0.01x2 Solving for variable 'x'. Combine like terms: 299 + -200 = 99 99 + -6x + -0.01x2 = 200 + 6x + 0.01x2 + -200 + -6x + -0.01x2 Reorder the terms: 99 + -6x + -0.01x2 = 200 + -200 + 6x + -6x + 0.01x2 + -0.01x2 Combine like terms: 200 + -200 = 0 99 + -6x + -0.01x2 = 0 + 6x + -6x + 0.01x2 + -0.01x2 99 + -6x + -0.01x2 = 6x + -6x + 0.01x2 + -0.01x2 Combine like terms: 6x + -6x = 0 99 + -6x + -0.01x2 = 0 + 0.01x2 + -0.01x2 99 + -6x + -0.01x2 = 0.01x2 + -0.01x2 Combine like terms: 0.01x2 + -0.01x2 = 0.00 99 + -6x + -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'. -9900 + 600x + x2 = 0 Move the constant term to the right: Add '9900' to each side of the equation. -9900 + 600x + 9900 + x2 = 0 + 9900 Reorder the terms: -9900 + 9900 + 600x + x2 = 0 + 9900 Combine like terms: -9900 + 9900 = 0 0 + 600x + x2 = 0 + 9900 600x + x2 = 0 + 9900 Combine like terms: 0 + 9900 = 9900 600x + x2 = 9900 The x term is 600x. Take half its coefficient (300). Square it (90000) and add it to both sides. Add '90000' to each side of the equation. 600x + 90000 + x2 = 9900 + 90000 Reorder the terms: 90000 + 600x + x2 = 9900 + 90000 Combine like terms: 9900 + 90000 = 99900 90000 + 600x + x2 = 99900 Factor a perfect square on the left side: (x + 300)(x + 300) = 99900 Calculate the square root of the right side: 316.069612586 Break this problem into two subproblems by setting (x + 300) equal to 316.069612586 and -316.069612586.Subproblem 1
x + 300 = 316.069612586 Simplifying x + 300 = 316.069612586 Reorder the terms: 300 + x = 316.069612586 Solving 300 + x = 316.069612586 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-300' to each side of the equation. 300 + -300 + x = 316.069612586 + -300 Combine like terms: 300 + -300 = 0 0 + x = 316.069612586 + -300 x = 316.069612586 + -300 Combine like terms: 316.069612586 + -300 = 16.069612586 x = 16.069612586 Simplifying x = 16.069612586Subproblem 2
x + 300 = -316.069612586 Simplifying x + 300 = -316.069612586 Reorder the terms: 300 + x = -316.069612586 Solving 300 + x = -316.069612586 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-300' to each side of the equation. 300 + -300 + x = -316.069612586 + -300 Combine like terms: 300 + -300 = 0 0 + x = -316.069612586 + -300 x = -316.069612586 + -300 Combine like terms: -316.069612586 + -300 = -616.069612586 x = -616.069612586 Simplifying x = -616.069612586Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.069612586, -616.069612586}
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