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Simplifying 2X2 + -13X + -64 = 0 Reorder the terms: -64 + -13X + 2X2 = 0 Solving -64 + -13X + 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 + -6.5X + X2 = 0 Move the constant term to the right: Add '32' to each side of the equation. -32 + -6.5X + 32 + X2 = 0 + 32 Reorder the terms: -32 + 32 + -6.5X + X2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -6.5X + X2 = 0 + 32 -6.5X + X2 = 0 + 32 Combine like terms: 0 + 32 = 32 -6.5X + X2 = 32 The X term is -6.5X. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5X + 10.5625 + X2 = 32 + 10.5625 Reorder the terms: 10.5625 + -6.5X + X2 = 32 + 10.5625 Combine like terms: 32 + 10.5625 = 42.5625 10.5625 + -6.5X + X2 = 42.5625 Factor a perfect square on the left side: (X + -3.25)(X + -3.25) = 42.5625 Calculate the square root of the right side: 6.523994175 Break this problem into two subproblems by setting (X + -3.25) equal to 6.523994175 and -6.523994175.Subproblem 1
X + -3.25 = 6.523994175 Simplifying X + -3.25 = 6.523994175 Reorder the terms: -3.25 + X = 6.523994175 Solving -3.25 + X = 6.523994175 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + X = 6.523994175 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + X = 6.523994175 + 3.25 X = 6.523994175 + 3.25 Combine like terms: 6.523994175 + 3.25 = 9.773994175 X = 9.773994175 Simplifying X = 9.773994175Subproblem 2
X + -3.25 = -6.523994175 Simplifying X + -3.25 = -6.523994175 Reorder the terms: -3.25 + X = -6.523994175 Solving -3.25 + X = -6.523994175 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + X = -6.523994175 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + X = -6.523994175 + 3.25 X = -6.523994175 + 3.25 Combine like terms: -6.523994175 + 3.25 = -3.273994175 X = -3.273994175 Simplifying X = -3.273994175Solution
The solution to the problem is based on the solutions from the subproblems. X = {9.773994175, -3.273994175}
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