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Simplifying 2x2 + 17x + 20 = 0 Reorder the terms: 20 + 17x + 2x2 = 0 Solving 20 + 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'. 10 + 8.5x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + 8.5x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + 8.5x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 8.5x + x2 = 0 + -10 8.5x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 8.5x + x2 = -10 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 = -10 + 18.0625 Reorder the terms: 18.0625 + 8.5x + x2 = -10 + 18.0625 Combine like terms: -10 + 18.0625 = 8.0625 18.0625 + 8.5x + x2 = 8.0625 Factor a perfect square on the left side: (x + 4.25)(x + 4.25) = 8.0625 Calculate the square root of the right side: 2.839454173 Break this problem into two subproblems by setting (x + 4.25) equal to 2.839454173 and -2.839454173.Subproblem 1
x + 4.25 = 2.839454173 Simplifying x + 4.25 = 2.839454173 Reorder the terms: 4.25 + x = 2.839454173 Solving 4.25 + x = 2.839454173 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 = 2.839454173 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = 2.839454173 + -4.25 x = 2.839454173 + -4.25 Combine like terms: 2.839454173 + -4.25 = -1.410545827 x = -1.410545827 Simplifying x = -1.410545827Subproblem 2
x + 4.25 = -2.839454173 Simplifying x + 4.25 = -2.839454173 Reorder the terms: 4.25 + x = -2.839454173 Solving 4.25 + x = -2.839454173 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 = -2.839454173 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = -2.839454173 + -4.25 x = -2.839454173 + -4.25 Combine like terms: -2.839454173 + -4.25 = -7.089454173 x = -7.089454173 Simplifying x = -7.089454173Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.410545827, -7.089454173}
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