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Simplifying 2x2 + -35x + -108 = 0 Reorder the terms: -108 + -35x + 2x2 = 0 Solving -108 + -35x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -54 + -17.5x + x2 = 0 Move the constant term to the right: Add '54' to each side of the equation. -54 + -17.5x + 54 + x2 = 0 + 54 Reorder the terms: -54 + 54 + -17.5x + x2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + -17.5x + x2 = 0 + 54 -17.5x + x2 = 0 + 54 Combine like terms: 0 + 54 = 54 -17.5x + x2 = 54 The x term is -17.5x. Take half its coefficient (-8.75). Square it (76.5625) and add it to both sides. Add '76.5625' to each side of the equation. -17.5x + 76.5625 + x2 = 54 + 76.5625 Reorder the terms: 76.5625 + -17.5x + x2 = 54 + 76.5625 Combine like terms: 54 + 76.5625 = 130.5625 76.5625 + -17.5x + x2 = 130.5625 Factor a perfect square on the left side: (x + -8.75)(x + -8.75) = 130.5625 Calculate the square root of the right side: 11.426394882 Break this problem into two subproblems by setting (x + -8.75) equal to 11.426394882 and -11.426394882.Subproblem 1
x + -8.75 = 11.426394882 Simplifying x + -8.75 = 11.426394882 Reorder the terms: -8.75 + x = 11.426394882 Solving -8.75 + x = 11.426394882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.75' to each side of the equation. -8.75 + 8.75 + x = 11.426394882 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + x = 11.426394882 + 8.75 x = 11.426394882 + 8.75 Combine like terms: 11.426394882 + 8.75 = 20.176394882 x = 20.176394882 Simplifying x = 20.176394882Subproblem 2
x + -8.75 = -11.426394882 Simplifying x + -8.75 = -11.426394882 Reorder the terms: -8.75 + x = -11.426394882 Solving -8.75 + x = -11.426394882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.75' to each side of the equation. -8.75 + 8.75 + x = -11.426394882 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + x = -11.426394882 + 8.75 x = -11.426394882 + 8.75 Combine like terms: -11.426394882 + 8.75 = -2.676394882 x = -2.676394882 Simplifying x = -2.676394882Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.176394882, -2.676394882}
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