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Simplifying 0.7X2 + -28X = 13014.30 Reorder the terms: -28X + 0.7X2 = 13014.30 Solving -28X + 0.7X2 = 13014.30 Solving for variable 'X'. Reorder the terms: -13014.30 + -28X + 0.7X2 = 13014.30 + -13014.30 Combine like terms: 13014.30 + -13014.30 = 0.00 -13014.30 + -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'. -18591.85714 + -40X + X2 = 0.0 Move the constant term to the right: Add '18591.85714' to each side of the equation. -18591.85714 + -40X + 18591.85714 + X2 = 0.0 + 18591.85714 Reorder the terms: -18591.85714 + 18591.85714 + -40X + X2 = 0.0 + 18591.85714 Combine like terms: -18591.85714 + 18591.85714 = 0.00000 0.00000 + -40X + X2 = 0.0 + 18591.85714 -40X + X2 = 0.0 + 18591.85714 Combine like terms: 0.0 + 18591.85714 = 18591.85714 -40X + X2 = 18591.85714 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 = 18591.85714 + 400 Reorder the terms: 400 + -40X + X2 = 18591.85714 + 400 Combine like terms: 18591.85714 + 400 = 18991.85714 400 + -40X + X2 = 18991.85714 Factor a perfect square on the left side: (X + -20)(X + -20) = 18991.85714 Calculate the square root of the right side: 137.810947098 Break this problem into two subproblems by setting (X + -20) equal to 137.810947098 and -137.810947098.Subproblem 1
X + -20 = 137.810947098 Simplifying X + -20 = 137.810947098 Reorder the terms: -20 + X = 137.810947098 Solving -20 + X = 137.810947098 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 = 137.810947098 + 20 Combine like terms: -20 + 20 = 0 0 + X = 137.810947098 + 20 X = 137.810947098 + 20 Combine like terms: 137.810947098 + 20 = 157.810947098 X = 157.810947098 Simplifying X = 157.810947098Subproblem 2
X + -20 = -137.810947098 Simplifying X + -20 = -137.810947098 Reorder the terms: -20 + X = -137.810947098 Solving -20 + X = -137.810947098 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 = -137.810947098 + 20 Combine like terms: -20 + 20 = 0 0 + X = -137.810947098 + 20 X = -137.810947098 + 20 Combine like terms: -137.810947098 + 20 = -117.810947098 X = -117.810947098 Simplifying X = -117.810947098Solution
The solution to the problem is based on the solutions from the subproblems. X = {157.810947098, -117.810947098}
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