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Simplifying 0.7x2 + -28x + 12000 = 13014.13 Reorder the terms: 12000 + -28x + 0.7x2 = 13014.13 Solving 12000 + -28x + 0.7x2 = 13014.13 Solving for variable 'x'. Reorder the terms: 12000 + -13014.13 + -28x + 0.7x2 = 13014.13 + -13014.13 Combine like terms: 12000 + -13014.13 = -1014.13 -1014.13 + -28x + 0.7x2 = 13014.13 + -13014.13 Combine like terms: 13014.13 + -13014.13 = 0.00 -1014.13 + -28x + 0.7x2 = 0.00 Begin completing the square. Divide all terms by 0.7 the coefficient of the squared term: Divide each side by '0.7'. -1448.757143 + -40x + x2 = 0.0 Move the constant term to the right: Add '1448.757143' to each side of the equation. -1448.757143 + -40x + 1448.757143 + x2 = 0.0 + 1448.757143 Reorder the terms: -1448.757143 + 1448.757143 + -40x + x2 = 0.0 + 1448.757143 Combine like terms: -1448.757143 + 1448.757143 = 0.000000 0.000000 + -40x + x2 = 0.0 + 1448.757143 -40x + x2 = 0.0 + 1448.757143 Combine like terms: 0.0 + 1448.757143 = 1448.757143 -40x + x2 = 1448.757143 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 = 1448.757143 + 400 Reorder the terms: 400 + -40x + x2 = 1448.757143 + 400 Combine like terms: 1448.757143 + 400 = 1848.757143 400 + -40x + x2 = 1848.757143 Factor a perfect square on the left side: (x + -20)(x + -20) = 1848.757143 Calculate the square root of the right side: 42.997175989 Break this problem into two subproblems by setting (x + -20) equal to 42.997175989 and -42.997175989.Subproblem 1
x + -20 = 42.997175989 Simplifying x + -20 = 42.997175989 Reorder the terms: -20 + x = 42.997175989 Solving -20 + x = 42.997175989 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 = 42.997175989 + 20 Combine like terms: -20 + 20 = 0 0 + x = 42.997175989 + 20 x = 42.997175989 + 20 Combine like terms: 42.997175989 + 20 = 62.997175989 x = 62.997175989 Simplifying x = 62.997175989Subproblem 2
x + -20 = -42.997175989 Simplifying x + -20 = -42.997175989 Reorder the terms: -20 + x = -42.997175989 Solving -20 + x = -42.997175989 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 = -42.997175989 + 20 Combine like terms: -20 + 20 = 0 0 + x = -42.997175989 + 20 x = -42.997175989 + 20 Combine like terms: -42.997175989 + 20 = -22.997175989 x = -22.997175989 Simplifying x = -22.997175989Solution
The solution to the problem is based on the solutions from the subproblems. x = {62.997175989, -22.997175989}
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