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Simplifying 2x2 + -5x + -17 = 0 Reorder the terms: -17 + -5x + 2x2 = 0 Solving -17 + -5x + 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'. -8.5 + -2.5x + x2 = 0 Move the constant term to the right: Add '8.5' to each side of the equation. -8.5 + -2.5x + 8.5 + x2 = 0 + 8.5 Reorder the terms: -8.5 + 8.5 + -2.5x + x2 = 0 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + -2.5x + x2 = 0 + 8.5 -2.5x + x2 = 0 + 8.5 Combine like terms: 0 + 8.5 = 8.5 -2.5x + x2 = 8.5 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 8.5 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 8.5 + 1.5625 Combine like terms: 8.5 + 1.5625 = 10.0625 1.5625 + -2.5x + x2 = 10.0625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 10.0625 Calculate the square root of the right side: 3.172144385 Break this problem into two subproblems by setting (x + -1.25) equal to 3.172144385 and -3.172144385.Subproblem 1
x + -1.25 = 3.172144385 Simplifying x + -1.25 = 3.172144385 Reorder the terms: -1.25 + x = 3.172144385 Solving -1.25 + x = 3.172144385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 3.172144385 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 3.172144385 + 1.25 x = 3.172144385 + 1.25 Combine like terms: 3.172144385 + 1.25 = 4.422144385 x = 4.422144385 Simplifying x = 4.422144385Subproblem 2
x + -1.25 = -3.172144385 Simplifying x + -1.25 = -3.172144385 Reorder the terms: -1.25 + x = -3.172144385 Solving -1.25 + x = -3.172144385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -3.172144385 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -3.172144385 + 1.25 x = -3.172144385 + 1.25 Combine like terms: -3.172144385 + 1.25 = -1.922144385 x = -1.922144385 Simplifying x = -1.922144385Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.422144385, -1.922144385}
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