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Simplifying 2x2 + -9x + -65 = 0 Reorder the terms: -65 + -9x + 2x2 = 0 Solving -65 + -9x + 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'. -32.5 + -4.5x + x2 = 0 Move the constant term to the right: Add '32.5' to each side of the equation. -32.5 + -4.5x + 32.5 + x2 = 0 + 32.5 Reorder the terms: -32.5 + 32.5 + -4.5x + x2 = 0 + 32.5 Combine like terms: -32.5 + 32.5 = 0.0 0.0 + -4.5x + x2 = 0 + 32.5 -4.5x + x2 = 0 + 32.5 Combine like terms: 0 + 32.5 = 32.5 -4.5x + x2 = 32.5 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = 32.5 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 32.5 + 5.0625 Combine like terms: 32.5 + 5.0625 = 37.5625 5.0625 + -4.5x + x2 = 37.5625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 37.5625 Calculate the square root of the right side: 6.128825336 Break this problem into two subproblems by setting (x + -2.25) equal to 6.128825336 and -6.128825336.Subproblem 1
x + -2.25 = 6.128825336 Simplifying x + -2.25 = 6.128825336 Reorder the terms: -2.25 + x = 6.128825336 Solving -2.25 + x = 6.128825336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 6.128825336 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 6.128825336 + 2.25 x = 6.128825336 + 2.25 Combine like terms: 6.128825336 + 2.25 = 8.378825336 x = 8.378825336 Simplifying x = 8.378825336Subproblem 2
x + -2.25 = -6.128825336 Simplifying x + -2.25 = -6.128825336 Reorder the terms: -2.25 + x = -6.128825336 Solving -2.25 + x = -6.128825336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -6.128825336 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -6.128825336 + 2.25 x = -6.128825336 + 2.25 Combine like terms: -6.128825336 + 2.25 = -3.878825336 x = -3.878825336 Simplifying x = -3.878825336Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.378825336, -3.878825336}
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