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Simplifying 11790 = 0.7x2 + -28x + 12000 Reorder the terms: 11790 = 12000 + -28x + 0.7x2 Solving 11790 = 12000 + -28x + 0.7x2 Solving for variable 'x'. Combine like terms: 11790 + -12000 = -210 -210 + 28x + -0.7x2 = 12000 + -28x + 0.7x2 + -12000 + 28x + -0.7x2 Reorder the terms: -210 + 28x + -0.7x2 = 12000 + -12000 + -28x + 28x + 0.7x2 + -0.7x2 Combine like terms: 12000 + -12000 = 0 -210 + 28x + -0.7x2 = 0 + -28x + 28x + 0.7x2 + -0.7x2 -210 + 28x + -0.7x2 = -28x + 28x + 0.7x2 + -0.7x2 Combine like terms: -28x + 28x = 0 -210 + 28x + -0.7x2 = 0 + 0.7x2 + -0.7x2 -210 + 28x + -0.7x2 = 0.7x2 + -0.7x2 Combine like terms: 0.7x2 + -0.7x2 = 0.0 -210 + 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'. 300 + -40x + x2 = 0 Move the constant term to the right: Add '-300' to each side of the equation. 300 + -40x + -300 + x2 = 0 + -300 Reorder the terms: 300 + -300 + -40x + x2 = 0 + -300 Combine like terms: 300 + -300 = 0 0 + -40x + x2 = 0 + -300 -40x + x2 = 0 + -300 Combine like terms: 0 + -300 = -300 -40x + x2 = -300 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 = -300 + 400 Reorder the terms: 400 + -40x + x2 = -300 + 400 Combine like terms: -300 + 400 = 100 400 + -40x + x2 = 100 Factor a perfect square on the left side: (x + -20)(x + -20) = 100 Calculate the square root of the right side: 10 Break this problem into two subproblems by setting (x + -20) equal to 10 and -10.Subproblem 1
x + -20 = 10 Simplifying x + -20 = 10 Reorder the terms: -20 + x = 10 Solving -20 + x = 10 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 = 10 + 20 Combine like terms: -20 + 20 = 0 0 + x = 10 + 20 x = 10 + 20 Combine like terms: 10 + 20 = 30 x = 30 Simplifying x = 30Subproblem 2
x + -20 = -10 Simplifying x + -20 = -10 Reorder the terms: -20 + x = -10 Solving -20 + x = -10 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 = -10 + 20 Combine like terms: -20 + 20 = 0 0 + x = -10 + 20 x = -10 + 20 Combine like terms: -10 + 20 = 10 x = 10 Simplifying x = 10Solution
The solution to the problem is based on the solutions from the subproblems. x = {30, 10}
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