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Simplifying 2x2 + 17x + -54 = 0 Reorder the terms: -54 + 17x + 2x2 = 0 Solving -54 + 17x + 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'. -27 + 8.5x + x2 = 0 Move the constant term to the right: Add '27' to each side of the equation. -27 + 8.5x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + 8.5x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 8.5x + x2 = 0 + 27 8.5x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 8.5x + x2 = 27 The x term is 8.5x. Take half its coefficient (4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. 8.5x + 18.0625 + x2 = 27 + 18.0625 Reorder the terms: 18.0625 + 8.5x + x2 = 27 + 18.0625 Combine like terms: 27 + 18.0625 = 45.0625 18.0625 + 8.5x + x2 = 45.0625 Factor a perfect square on the left side: (x + 4.25)(x + 4.25) = 45.0625 Calculate the square root of the right side: 6.712860791 Break this problem into two subproblems by setting (x + 4.25) equal to 6.712860791 and -6.712860791.Subproblem 1
x + 4.25 = 6.712860791 Simplifying x + 4.25 = 6.712860791 Reorder the terms: 4.25 + x = 6.712860791 Solving 4.25 + x = 6.712860791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = 6.712860791 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = 6.712860791 + -4.25 x = 6.712860791 + -4.25 Combine like terms: 6.712860791 + -4.25 = 2.462860791 x = 2.462860791 Simplifying x = 2.462860791Subproblem 2
x + 4.25 = -6.712860791 Simplifying x + 4.25 = -6.712860791 Reorder the terms: 4.25 + x = -6.712860791 Solving 4.25 + x = -6.712860791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = -6.712860791 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = -6.712860791 + -4.25 x = -6.712860791 + -4.25 Combine like terms: -6.712860791 + -4.25 = -10.962860791 x = -10.962860791 Simplifying x = -10.962860791Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.462860791, -10.962860791}
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