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Simplifying 5x2 + -1728x + -5184 = 0 Reorder the terms: -5184 + -1728x + 5x2 = 0 Solving -5184 + -1728x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1036.8 + -345.6x + x2 = 0 Move the constant term to the right: Add '1036.8' to each side of the equation. -1036.8 + -345.6x + 1036.8 + x2 = 0 + 1036.8 Reorder the terms: -1036.8 + 1036.8 + -345.6x + x2 = 0 + 1036.8 Combine like terms: -1036.8 + 1036.8 = 0.0 0.0 + -345.6x + x2 = 0 + 1036.8 -345.6x + x2 = 0 + 1036.8 Combine like terms: 0 + 1036.8 = 1036.8 -345.6x + x2 = 1036.8 The x term is -345.6x. Take half its coefficient (-172.8). Square it (29859.84) and add it to both sides. Add '29859.84' to each side of the equation. -345.6x + 29859.84 + x2 = 1036.8 + 29859.84 Reorder the terms: 29859.84 + -345.6x + x2 = 1036.8 + 29859.84 Combine like terms: 1036.8 + 29859.84 = 30896.64 29859.84 + -345.6x + x2 = 30896.64 Factor a perfect square on the left side: (x + -172.8)(x + -172.8) = 30896.64 Calculate the square root of the right side: 175.774400867 Break this problem into two subproblems by setting (x + -172.8) equal to 175.774400867 and -175.774400867.Subproblem 1
x + -172.8 = 175.774400867 Simplifying x + -172.8 = 175.774400867 Reorder the terms: -172.8 + x = 175.774400867 Solving -172.8 + x = 175.774400867 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '172.8' to each side of the equation. -172.8 + 172.8 + x = 175.774400867 + 172.8 Combine like terms: -172.8 + 172.8 = 0.0 0.0 + x = 175.774400867 + 172.8 x = 175.774400867 + 172.8 Combine like terms: 175.774400867 + 172.8 = 348.574400867 x = 348.574400867 Simplifying x = 348.574400867Subproblem 2
x + -172.8 = -175.774400867 Simplifying x + -172.8 = -175.774400867 Reorder the terms: -172.8 + x = -175.774400867 Solving -172.8 + x = -175.774400867 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '172.8' to each side of the equation. -172.8 + 172.8 + x = -175.774400867 + 172.8 Combine like terms: -172.8 + 172.8 = 0.0 0.0 + x = -175.774400867 + 172.8 x = -175.774400867 + 172.8 Combine like terms: -175.774400867 + 172.8 = -2.974400867 x = -2.974400867 Simplifying x = -2.974400867Solution
The solution to the problem is based on the solutions from the subproblems. x = {348.574400867, -2.974400867}
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