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Simplifying 9x + -0.06x2 = 300 Solving 9x + -0.06x2 = 300 Solving for variable 'x'. Reorder the terms: -300 + 9x + -0.06x2 = 300 + -300 Combine like terms: 300 + -300 = 0 -300 + 9x + -0.06x2 = 0 Begin completing the square. Divide all terms by -0.06 the coefficient of the squared term: Divide each side by '-0.06'. 5000 + -150x + x2 = 0 Move the constant term to the right: Add '-5000' to each side of the equation. 5000 + -150x + -5000 + x2 = 0 + -5000 Reorder the terms: 5000 + -5000 + -150x + x2 = 0 + -5000 Combine like terms: 5000 + -5000 = 0 0 + -150x + x2 = 0 + -5000 -150x + x2 = 0 + -5000 Combine like terms: 0 + -5000 = -5000 -150x + x2 = -5000 The x term is -150x. Take half its coefficient (-75). Square it (5625) and add it to both sides. Add '5625' to each side of the equation. -150x + 5625 + x2 = -5000 + 5625 Reorder the terms: 5625 + -150x + x2 = -5000 + 5625 Combine like terms: -5000 + 5625 = 625 5625 + -150x + x2 = 625 Factor a perfect square on the left side: (x + -75)(x + -75) = 625 Calculate the square root of the right side: 25 Break this problem into two subproblems by setting (x + -75) equal to 25 and -25.Subproblem 1
x + -75 = 25 Simplifying x + -75 = 25 Reorder the terms: -75 + x = 25 Solving -75 + x = 25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '75' to each side of the equation. -75 + 75 + x = 25 + 75 Combine like terms: -75 + 75 = 0 0 + x = 25 + 75 x = 25 + 75 Combine like terms: 25 + 75 = 100 x = 100 Simplifying x = 100Subproblem 2
x + -75 = -25 Simplifying x + -75 = -25 Reorder the terms: -75 + x = -25 Solving -75 + x = -25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '75' to each side of the equation. -75 + 75 + x = -25 + 75 Combine like terms: -75 + 75 = 0 0 + x = -25 + 75 x = -25 + 75 Combine like terms: -25 + 75 = 50 x = 50 Simplifying x = 50Solution
The solution to the problem is based on the solutions from the subproblems. x = {100, 50}
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