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Simplifying 2(x2) + -16x + 17 = 0 Reorder the terms: 17 + -16x + 2x2 = 0 Solving 17 + -16x + 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 + -8x + x2 = 0 Move the constant term to the right: Add '-8.5' to each side of the equation. 8.5 + -8x + -8.5 + x2 = 0 + -8.5 Reorder the terms: 8.5 + -8.5 + -8x + x2 = 0 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + -8x + x2 = 0 + -8.5 -8x + x2 = 0 + -8.5 Combine like terms: 0 + -8.5 = -8.5 -8x + x2 = -8.5 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -8.5 + 16 Reorder the terms: 16 + -8x + x2 = -8.5 + 16 Combine like terms: -8.5 + 16 = 7.5 16 + -8x + x2 = 7.5 Factor a perfect square on the left side: (x + -4)(x + -4) = 7.5 Calculate the square root of the right side: 2.738612788 Break this problem into two subproblems by setting (x + -4) equal to 2.738612788 and -2.738612788.Subproblem 1
x + -4 = 2.738612788 Simplifying x + -4 = 2.738612788 Reorder the terms: -4 + x = 2.738612788 Solving -4 + x = 2.738612788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 2.738612788 + 4 Combine like terms: -4 + 4 = 0 0 + x = 2.738612788 + 4 x = 2.738612788 + 4 Combine like terms: 2.738612788 + 4 = 6.738612788 x = 6.738612788 Simplifying x = 6.738612788Subproblem 2
x + -4 = -2.738612788 Simplifying x + -4 = -2.738612788 Reorder the terms: -4 + x = -2.738612788 Solving -4 + x = -2.738612788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -2.738612788 + 4 Combine like terms: -4 + 4 = 0 0 + x = -2.738612788 + 4 x = -2.738612788 + 4 Combine like terms: -2.738612788 + 4 = 1.261387212 x = 1.261387212 Simplifying x = 1.261387212Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.738612788, 1.261387212}
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