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Simplifying 2x2 + -11x + -17 = 0 Reorder the terms: -17 + -11x + 2x2 = 0 Solving -17 + -11x + 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 + -5.5x + x2 = 0 Move the constant term to the right: Add '8.5' to each side of the equation. -8.5 + -5.5x + 8.5 + x2 = 0 + 8.5 Reorder the terms: -8.5 + 8.5 + -5.5x + x2 = 0 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + -5.5x + x2 = 0 + 8.5 -5.5x + x2 = 0 + 8.5 Combine like terms: 0 + 8.5 = 8.5 -5.5x + x2 = 8.5 The x term is -5.5x. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5x + 7.5625 + x2 = 8.5 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = 8.5 + 7.5625 Combine like terms: 8.5 + 7.5625 = 16.0625 7.5625 + -5.5x + x2 = 16.0625 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 16.0625 Calculate the square root of the right side: 4.007804885 Break this problem into two subproblems by setting (x + -2.75) equal to 4.007804885 and -4.007804885.Subproblem 1
x + -2.75 = 4.007804885 Simplifying x + -2.75 = 4.007804885 Reorder the terms: -2.75 + x = 4.007804885 Solving -2.75 + x = 4.007804885 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 4.007804885 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 4.007804885 + 2.75 x = 4.007804885 + 2.75 Combine like terms: 4.007804885 + 2.75 = 6.757804885 x = 6.757804885 Simplifying x = 6.757804885Subproblem 2
x + -2.75 = -4.007804885 Simplifying x + -2.75 = -4.007804885 Reorder the terms: -2.75 + x = -4.007804885 Solving -2.75 + x = -4.007804885 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -4.007804885 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -4.007804885 + 2.75 x = -4.007804885 + 2.75 Combine like terms: -4.007804885 + 2.75 = -1.257804885 x = -1.257804885 Simplifying x = -1.257804885Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.757804885, -1.257804885}
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