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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 = 7.089454173 x = 7.089454173 Simplifying x = 7.089454173Subproblem 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 = 1.410545827 x = 1.410545827 Simplifying x = 1.410545827Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.089454173, 1.410545827}
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