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Simplifying 141 = 200 + 6x + 0.01x2 Solving 141 = 200 + 6x + 0.01x2 Solving for variable 'x'. Combine like terms: 141 + -200 = -59 -59 + -6x + -0.01x2 = 200 + 6x + 0.01x2 + -200 + -6x + -0.01x2 Reorder the terms: -59 + -6x + -0.01x2 = 200 + -200 + 6x + -6x + 0.01x2 + -0.01x2 Combine like terms: 200 + -200 = 0 -59 + -6x + -0.01x2 = 0 + 6x + -6x + 0.01x2 + -0.01x2 -59 + -6x + -0.01x2 = 6x + -6x + 0.01x2 + -0.01x2 Combine like terms: 6x + -6x = 0 -59 + -6x + -0.01x2 = 0 + 0.01x2 + -0.01x2 -59 + -6x + -0.01x2 = 0.01x2 + -0.01x2 Combine like terms: 0.01x2 + -0.01x2 = 0.00 -59 + -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'. 5900 + 600x + x2 = 0 Move the constant term to the right: Add '-5900' to each side of the equation. 5900 + 600x + -5900 + x2 = 0 + -5900 Reorder the terms: 5900 + -5900 + 600x + x2 = 0 + -5900 Combine like terms: 5900 + -5900 = 0 0 + 600x + x2 = 0 + -5900 600x + x2 = 0 + -5900 Combine like terms: 0 + -5900 = -5900 600x + x2 = -5900 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 = -5900 + 90000 Reorder the terms: 90000 + 600x + x2 = -5900 + 90000 Combine like terms: -5900 + 90000 = 84100 90000 + 600x + x2 = 84100 Factor a perfect square on the left side: (x + 300)(x + 300) = 84100 Calculate the square root of the right side: 290 Break this problem into two subproblems by setting (x + 300) equal to 290 and -290.Subproblem 1
x + 300 = 290 Simplifying x + 300 = 290 Reorder the terms: 300 + x = 290 Solving 300 + x = 290 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 = 290 + -300 Combine like terms: 300 + -300 = 0 0 + x = 290 + -300 x = 290 + -300 Combine like terms: 290 + -300 = -10 x = -10 Simplifying x = -10Subproblem 2
x + 300 = -290 Simplifying x + 300 = -290 Reorder the terms: 300 + x = -290 Solving 300 + x = -290 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 = -290 + -300 Combine like terms: 300 + -300 = 0 0 + x = -290 + -300 x = -290 + -300 Combine like terms: -290 + -300 = -590 x = -590 Simplifying x = -590Solution
The solution to the problem is based on the solutions from the subproblems. x = {-10, -590}
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