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Simplifying 2x2 + -17x + -8 = 0 Reorder the terms: -8 + -17x + 2x2 = 0 Solving -8 + -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'. -4 + -8.5x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -8.5x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -8.5x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -8.5x + x2 = 0 + 4 -8.5x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -8.5x + x2 = 4 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 = 4 + 18.0625 Reorder the terms: 18.0625 + -8.5x + x2 = 4 + 18.0625 Combine like terms: 4 + 18.0625 = 22.0625 18.0625 + -8.5x + x2 = 22.0625 Factor a perfect square on the left side: (x + -4.25)(x + -4.25) = 22.0625 Calculate the square root of the right side: 4.697073557 Break this problem into two subproblems by setting (x + -4.25) equal to 4.697073557 and -4.697073557.Subproblem 1
x + -4.25 = 4.697073557 Simplifying x + -4.25 = 4.697073557 Reorder the terms: -4.25 + x = 4.697073557 Solving -4.25 + x = 4.697073557 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 = 4.697073557 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = 4.697073557 + 4.25 x = 4.697073557 + 4.25 Combine like terms: 4.697073557 + 4.25 = 8.947073557 x = 8.947073557 Simplifying x = 8.947073557Subproblem 2
x + -4.25 = -4.697073557 Simplifying x + -4.25 = -4.697073557 Reorder the terms: -4.25 + x = -4.697073557 Solving -4.25 + x = -4.697073557 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 = -4.697073557 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = -4.697073557 + 4.25 x = -4.697073557 + 4.25 Combine like terms: -4.697073557 + 4.25 = -0.447073557 x = -0.447073557 Simplifying x = -0.447073557Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.947073557, -0.447073557}
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