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Simplifying 2x2 + 33x + -28 = 0 Reorder the terms: -28 + 33x + 2x2 = 0 Solving -28 + 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'. -14 + 16.5x + x2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + 16.5x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + 16.5x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 16.5x + x2 = 0 + 14 16.5x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 16.5x + x2 = 14 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 = 14 + 68.0625 Reorder the terms: 68.0625 + 16.5x + x2 = 14 + 68.0625 Combine like terms: 14 + 68.0625 = 82.0625 68.0625 + 16.5x + x2 = 82.0625 Factor a perfect square on the left side: (x + 8.25)(x + 8.25) = 82.0625 Calculate the square root of the right side: 9.058835466 Break this problem into two subproblems by setting (x + 8.25) equal to 9.058835466 and -9.058835466.Subproblem 1
x + 8.25 = 9.058835466 Simplifying x + 8.25 = 9.058835466 Reorder the terms: 8.25 + x = 9.058835466 Solving 8.25 + x = 9.058835466 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 = 9.058835466 + -8.25 Combine like terms: 8.25 + -8.25 = 0.00 0.00 + x = 9.058835466 + -8.25 x = 9.058835466 + -8.25 Combine like terms: 9.058835466 + -8.25 = 0.808835466 x = 0.808835466 Simplifying x = 0.808835466Subproblem 2
x + 8.25 = -9.058835466 Simplifying x + 8.25 = -9.058835466 Reorder the terms: 8.25 + x = -9.058835466 Solving 8.25 + x = -9.058835466 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 = -9.058835466 + -8.25 Combine like terms: 8.25 + -8.25 = 0.00 0.00 + x = -9.058835466 + -8.25 x = -9.058835466 + -8.25 Combine like terms: -9.058835466 + -8.25 = -17.308835466 x = -17.308835466 Simplifying x = -17.308835466Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.808835466, -17.308835466}
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