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Simplifying 2x2 + 33x + -84 = 0 Reorder the terms: -84 + 33x + 2x2 = 0 Solving -84 + 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'. -42 + 16.5x + x2 = 0 Move the constant term to the right: Add '42' to each side of the equation. -42 + 16.5x + 42 + x2 = 0 + 42 Reorder the terms: -42 + 42 + 16.5x + x2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + 16.5x + x2 = 0 + 42 16.5x + x2 = 0 + 42 Combine like terms: 0 + 42 = 42 16.5x + x2 = 42 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 = 42 + 68.0625 Reorder the terms: 68.0625 + 16.5x + x2 = 42 + 68.0625 Combine like terms: 42 + 68.0625 = 110.0625 68.0625 + 16.5x + x2 = 110.0625 Factor a perfect square on the left side: (x + 8.25)(x + 8.25) = 110.0625 Calculate the square root of the right side: 10.491067629 Break this problem into two subproblems by setting (x + 8.25) equal to 10.491067629 and -10.491067629.Subproblem 1
x + 8.25 = 10.491067629 Simplifying x + 8.25 = 10.491067629 Reorder the terms: 8.25 + x = 10.491067629 Solving 8.25 + x = 10.491067629 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 = 10.491067629 + -8.25 Combine like terms: 8.25 + -8.25 = 0.00 0.00 + x = 10.491067629 + -8.25 x = 10.491067629 + -8.25 Combine like terms: 10.491067629 + -8.25 = 2.241067629 x = 2.241067629 Simplifying x = 2.241067629Subproblem 2
x + 8.25 = -10.491067629 Simplifying x + 8.25 = -10.491067629 Reorder the terms: 8.25 + x = -10.491067629 Solving 8.25 + x = -10.491067629 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 = -10.491067629 + -8.25 Combine like terms: 8.25 + -8.25 = 0.00 0.00 + x = -10.491067629 + -8.25 x = -10.491067629 + -8.25 Combine like terms: -10.491067629 + -8.25 = -18.741067629 x = -18.741067629 Simplifying x = -18.741067629Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.241067629, -18.741067629}
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