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Simplifying 3x2 + -600x + 22.5 = 0 Reorder the terms: 22.5 + -600x + 3x2 = 0 Solving 22.5 + -600x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 7.5 + -200x + x2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + -200x + -7.5 + x2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + -200x + x2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + -200x + x2 = 0 + -7.5 -200x + x2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 -200x + x2 = -7.5 The x term is -200x. Take half its coefficient (-100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. -200x + 10000 + x2 = -7.5 + 10000 Reorder the terms: 10000 + -200x + x2 = -7.5 + 10000 Combine like terms: -7.5 + 10000 = 9992.5 10000 + -200x + x2 = 9992.5 Factor a perfect square on the left side: (x + -100)(x + -100) = 9992.5 Calculate the square root of the right side: 99.962492966 Break this problem into two subproblems by setting (x + -100) equal to 99.962492966 and -99.962492966.Subproblem 1
x + -100 = 99.962492966 Simplifying x + -100 = 99.962492966 Reorder the terms: -100 + x = 99.962492966 Solving -100 + x = 99.962492966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = 99.962492966 + 100 Combine like terms: -100 + 100 = 0 0 + x = 99.962492966 + 100 x = 99.962492966 + 100 Combine like terms: 99.962492966 + 100 = 199.962492966 x = 199.962492966 Simplifying x = 199.962492966Subproblem 2
x + -100 = -99.962492966 Simplifying x + -100 = -99.962492966 Reorder the terms: -100 + x = -99.962492966 Solving -100 + x = -99.962492966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = -99.962492966 + 100 Combine like terms: -100 + 100 = 0 0 + x = -99.962492966 + 100 x = -99.962492966 + 100 Combine like terms: -99.962492966 + 100 = 0.037507034 x = 0.037507034 Simplifying x = 0.037507034Solution
The solution to the problem is based on the solutions from the subproblems. x = {199.962492966, 0.037507034}
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