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Simplifying 96 = 200 + 6x + 0.01x2 Solving 96 = 200 + 6x + 0.01x2 Solving for variable 'x'. Combine like terms: 96 + -200 = -104 -104 + -6x + -0.01x2 = 200 + 6x + 0.01x2 + -200 + -6x + -0.01x2 Reorder the terms: -104 + -6x + -0.01x2 = 200 + -200 + 6x + -6x + 0.01x2 + -0.01x2 Combine like terms: 200 + -200 = 0 -104 + -6x + -0.01x2 = 0 + 6x + -6x + 0.01x2 + -0.01x2 -104 + -6x + -0.01x2 = 6x + -6x + 0.01x2 + -0.01x2 Combine like terms: 6x + -6x = 0 -104 + -6x + -0.01x2 = 0 + 0.01x2 + -0.01x2 -104 + -6x + -0.01x2 = 0.01x2 + -0.01x2 Combine like terms: 0.01x2 + -0.01x2 = 0.00 -104 + -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'. 10400 + 600x + x2 = 0 Move the constant term to the right: Add '-10400' to each side of the equation. 10400 + 600x + -10400 + x2 = 0 + -10400 Reorder the terms: 10400 + -10400 + 600x + x2 = 0 + -10400 Combine like terms: 10400 + -10400 = 0 0 + 600x + x2 = 0 + -10400 600x + x2 = 0 + -10400 Combine like terms: 0 + -10400 = -10400 600x + x2 = -10400 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 = -10400 + 90000 Reorder the terms: 90000 + 600x + x2 = -10400 + 90000 Combine like terms: -10400 + 90000 = 79600 90000 + 600x + x2 = 79600 Factor a perfect square on the left side: (x + 300)(x + 300) = 79600 Calculate the square root of the right side: 282.134719593 Break this problem into two subproblems by setting (x + 300) equal to 282.134719593 and -282.134719593.Subproblem 1
x + 300 = 282.134719593 Simplifying x + 300 = 282.134719593 Reorder the terms: 300 + x = 282.134719593 Solving 300 + x = 282.134719593 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 = 282.134719593 + -300 Combine like terms: 300 + -300 = 0 0 + x = 282.134719593 + -300 x = 282.134719593 + -300 Combine like terms: 282.134719593 + -300 = -17.865280407 x = -17.865280407 Simplifying x = -17.865280407Subproblem 2
x + 300 = -282.134719593 Simplifying x + 300 = -282.134719593 Reorder the terms: 300 + x = -282.134719593 Solving 300 + x = -282.134719593 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 = -282.134719593 + -300 Combine like terms: 300 + -300 = 0 0 + x = -282.134719593 + -300 x = -282.134719593 + -300 Combine like terms: -282.134719593 + -300 = -582.134719593 x = -582.134719593 Simplifying x = -582.134719593Solution
The solution to the problem is based on the solutions from the subproblems. x = {-17.865280407, -582.134719593}
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