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Simplifying 2x2 + -17x + 16 = 0 Reorder the terms: 16 + -17x + 2x2 = 0 Solving 16 + -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'. 8 + -8.5x + x2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + -8.5x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -8.5x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -8.5x + x2 = 0 + -8 -8.5x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -8.5x + x2 = -8 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 = -8 + 18.0625 Reorder the terms: 18.0625 + -8.5x + x2 = -8 + 18.0625 Combine like terms: -8 + 18.0625 = 10.0625 18.0625 + -8.5x + x2 = 10.0625 Factor a perfect square on the left side: (x + -4.25)(x + -4.25) = 10.0625 Calculate the square root of the right side: 3.172144385 Break this problem into two subproblems by setting (x + -4.25) equal to 3.172144385 and -3.172144385.Subproblem 1
x + -4.25 = 3.172144385 Simplifying x + -4.25 = 3.172144385 Reorder the terms: -4.25 + x = 3.172144385 Solving -4.25 + x = 3.172144385 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 = 3.172144385 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = 3.172144385 + 4.25 x = 3.172144385 + 4.25 Combine like terms: 3.172144385 + 4.25 = 7.422144385 x = 7.422144385 Simplifying x = 7.422144385Subproblem 2
x + -4.25 = -3.172144385 Simplifying x + -4.25 = -3.172144385 Reorder the terms: -4.25 + x = -3.172144385 Solving -4.25 + x = -3.172144385 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 = -3.172144385 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = -3.172144385 + 4.25 x = -3.172144385 + 4.25 Combine like terms: -3.172144385 + 4.25 = 1.077855615 x = 1.077855615 Simplifying x = 1.077855615Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.422144385, 1.077855615}
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