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Simplifying 2x2 + 33x + -6.5 = 0 Reorder the terms: -6.5 + 33x + 2x2 = 0 Solving -6.5 + 33x + 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'. -3.25 + 16.5x + x2 = 0 Move the constant term to the right: Add '3.25' to each side of the equation. -3.25 + 16.5x + 3.25 + x2 = 0 + 3.25 Reorder the terms: -3.25 + 3.25 + 16.5x + x2 = 0 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + 16.5x + x2 = 0 + 3.25 16.5x + x2 = 0 + 3.25 Combine like terms: 0 + 3.25 = 3.25 16.5x + x2 = 3.25 The x term is 16.5x. Take half its coefficient (8.25). Square it (68.0625) and add it to both sides. Add '68.0625' to each side of the equation. 16.5x + 68.0625 + x2 = 3.25 + 68.0625 Reorder the terms: 68.0625 + 16.5x + x2 = 3.25 + 68.0625 Combine like terms: 3.25 + 68.0625 = 71.3125 68.0625 + 16.5x + x2 = 71.3125 Factor a perfect square on the left side: (x + 8.25)(x + 8.25) = 71.3125 Calculate the square root of the right side: 8.444672877 Break this problem into two subproblems by setting (x + 8.25) equal to 8.444672877 and -8.444672877.Subproblem 1
x + 8.25 = 8.444672877 Simplifying x + 8.25 = 8.444672877 Reorder the terms: 8.25 + x = 8.444672877 Solving 8.25 + x = 8.444672877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.25' to each side of the equation. 8.25 + -8.25 + x = 8.444672877 + -8.25 Combine like terms: 8.25 + -8.25 = 0.00 0.00 + x = 8.444672877 + -8.25 x = 8.444672877 + -8.25 Combine like terms: 8.444672877 + -8.25 = 0.194672877 x = 0.194672877 Simplifying x = 0.194672877Subproblem 2
x + 8.25 = -8.444672877 Simplifying x + 8.25 = -8.444672877 Reorder the terms: 8.25 + x = -8.444672877 Solving 8.25 + x = -8.444672877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.25' to each side of the equation. 8.25 + -8.25 + x = -8.444672877 + -8.25 Combine like terms: 8.25 + -8.25 = 0.00 0.00 + x = -8.444672877 + -8.25 x = -8.444672877 + -8.25 Combine like terms: -8.444672877 + -8.25 = -16.694672877 x = -16.694672877 Simplifying x = -16.694672877Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.194672877, -16.694672877}
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