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Simplifying 0.05x2 + -6x + 64.8 = 12 Reorder the terms: 64.8 + -6x + 0.05x2 = 12 Solving 64.8 + -6x + 0.05x2 = 12 Solving for variable 'x'. Reorder the terms: 64.8 + -12 + -6x + 0.05x2 = 12 + -12 Combine like terms: 64.8 + -12 = 52.8 52.8 + -6x + 0.05x2 = 12 + -12 Combine like terms: 12 + -12 = 0 52.8 + -6x + 0.05x2 = 0 Begin completing the square. Divide all terms by 0.05 the coefficient of the squared term: Divide each side by '0.05'. 1056 + -120x + x2 = 0 Move the constant term to the right: Add '-1056' to each side of the equation. 1056 + -120x + -1056 + x2 = 0 + -1056 Reorder the terms: 1056 + -1056 + -120x + x2 = 0 + -1056 Combine like terms: 1056 + -1056 = 0 0 + -120x + x2 = 0 + -1056 -120x + x2 = 0 + -1056 Combine like terms: 0 + -1056 = -1056 -120x + x2 = -1056 The x term is -120x. Take half its coefficient (-60). Square it (3600) and add it to both sides. Add '3600' to each side of the equation. -120x + 3600 + x2 = -1056 + 3600 Reorder the terms: 3600 + -120x + x2 = -1056 + 3600 Combine like terms: -1056 + 3600 = 2544 3600 + -120x + x2 = 2544 Factor a perfect square on the left side: (x + -60)(x + -60) = 2544 Calculate the square root of the right side: 50.438080852 Break this problem into two subproblems by setting (x + -60) equal to 50.438080852 and -50.438080852.Subproblem 1
x + -60 = 50.438080852 Simplifying x + -60 = 50.438080852 Reorder the terms: -60 + x = 50.438080852 Solving -60 + x = 50.438080852 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '60' to each side of the equation. -60 + 60 + x = 50.438080852 + 60 Combine like terms: -60 + 60 = 0 0 + x = 50.438080852 + 60 x = 50.438080852 + 60 Combine like terms: 50.438080852 + 60 = 110.438080852 x = 110.438080852 Simplifying x = 110.438080852Subproblem 2
x + -60 = -50.438080852 Simplifying x + -60 = -50.438080852 Reorder the terms: -60 + x = -50.438080852 Solving -60 + x = -50.438080852 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '60' to each side of the equation. -60 + 60 + x = -50.438080852 + 60 Combine like terms: -60 + 60 = 0 0 + x = -50.438080852 + 60 x = -50.438080852 + 60 Combine like terms: -50.438080852 + 60 = 9.561919148 x = 9.561919148 Simplifying x = 9.561919148Solution
The solution to the problem is based on the solutions from the subproblems. x = {110.438080852, 9.561919148}
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