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Simplifying 0.7x2 + -28x + 12000 = 13014.3 Reorder the terms: 12000 + -28x + 0.7x2 = 13014.3 Solving 12000 + -28x + 0.7x2 = 13014.3 Solving for variable 'x'. Reorder the terms: 12000 + -13014.3 + -28x + 0.7x2 = 13014.3 + -13014.3 Combine like terms: 12000 + -13014.3 = -1014.3 -1014.3 + -28x + 0.7x2 = 13014.3 + -13014.3 Combine like terms: 13014.3 + -13014.3 = 0.0 -1014.3 + -28x + 0.7x2 = 0.0 Begin completing the square. Divide all terms by 0.7 the coefficient of the squared term: Divide each side by '0.7'. -1449 + -40x + x2 = 0 Move the constant term to the right: Add '1449' to each side of the equation. -1449 + -40x + 1449 + x2 = 0 + 1449 Reorder the terms: -1449 + 1449 + -40x + x2 = 0 + 1449 Combine like terms: -1449 + 1449 = 0 0 + -40x + x2 = 0 + 1449 -40x + x2 = 0 + 1449 Combine like terms: 0 + 1449 = 1449 -40x + x2 = 1449 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = 1449 + 400 Reorder the terms: 400 + -40x + x2 = 1449 + 400 Combine like terms: 1449 + 400 = 1849 400 + -40x + x2 = 1849 Factor a perfect square on the left side: (x + -20)(x + -20) = 1849 Calculate the square root of the right side: 43 Break this problem into two subproblems by setting (x + -20) equal to 43 and -43.Subproblem 1
x + -20 = 43 Simplifying x + -20 = 43 Reorder the terms: -20 + x = 43 Solving -20 + x = 43 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 43 + 20 Combine like terms: -20 + 20 = 0 0 + x = 43 + 20 x = 43 + 20 Combine like terms: 43 + 20 = 63 x = 63 Simplifying x = 63Subproblem 2
x + -20 = -43 Simplifying x + -20 = -43 Reorder the terms: -20 + x = -43 Solving -20 + x = -43 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -43 + 20 Combine like terms: -20 + 20 = 0 0 + x = -43 + 20 x = -43 + 20 Combine like terms: -43 + 20 = -23 x = -23 Simplifying x = -23Solution
The solution to the problem is based on the solutions from the subproblems. x = {63, -23}
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