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Simplifying 2x2 + -5x + -195 = 0 Reorder the terms: -195 + -5x + 2x2 = 0 Solving -195 + -5x + 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'. -97.5 + -2.5x + x2 = 0 Move the constant term to the right: Add '97.5' to each side of the equation. -97.5 + -2.5x + 97.5 + x2 = 0 + 97.5 Reorder the terms: -97.5 + 97.5 + -2.5x + x2 = 0 + 97.5 Combine like terms: -97.5 + 97.5 = 0.0 0.0 + -2.5x + x2 = 0 + 97.5 -2.5x + x2 = 0 + 97.5 Combine like terms: 0 + 97.5 = 97.5 -2.5x + x2 = 97.5 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 97.5 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 97.5 + 1.5625 Combine like terms: 97.5 + 1.5625 = 99.0625 1.5625 + -2.5x + x2 = 99.0625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 99.0625 Calculate the square root of the right side: 9.953014619 Break this problem into two subproblems by setting (x + -1.25) equal to 9.953014619 and -9.953014619.Subproblem 1
x + -1.25 = 9.953014619 Simplifying x + -1.25 = 9.953014619 Reorder the terms: -1.25 + x = 9.953014619 Solving -1.25 + x = 9.953014619 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 9.953014619 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 9.953014619 + 1.25 x = 9.953014619 + 1.25 Combine like terms: 9.953014619 + 1.25 = 11.203014619 x = 11.203014619 Simplifying x = 11.203014619Subproblem 2
x + -1.25 = -9.953014619 Simplifying x + -1.25 = -9.953014619 Reorder the terms: -1.25 + x = -9.953014619 Solving -1.25 + x = -9.953014619 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -9.953014619 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -9.953014619 + 1.25 x = -9.953014619 + 1.25 Combine like terms: -9.953014619 + 1.25 = -8.703014619 x = -8.703014619 Simplifying x = -8.703014619Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.203014619, -8.703014619}
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