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Simplifying 17 = 8y(y + -2) Reorder the terms: 17 = 8y(-2 + y) 17 = (-2 * 8y + y * 8y) 17 = (-16y + 8y2) Solving 17 = -16y + 8y2 Solving for variable 'y'. Reorder the terms: 17 + 16y + -8y2 = -16y + 16y + 8y2 + -8y2 Combine like terms: -16y + 16y = 0 17 + 16y + -8y2 = 0 + 8y2 + -8y2 17 + 16y + -8y2 = 8y2 + -8y2 Combine like terms: 8y2 + -8y2 = 0 17 + 16y + -8y2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -2.125 + -2y + y2 = 0 Move the constant term to the right: Add '2.125' to each side of the equation. -2.125 + -2y + 2.125 + y2 = 0 + 2.125 Reorder the terms: -2.125 + 2.125 + -2y + y2 = 0 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + -2y + y2 = 0 + 2.125 -2y + y2 = 0 + 2.125 Combine like terms: 0 + 2.125 = 2.125 -2y + y2 = 2.125 The y term is -2y. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2y + 1 + y2 = 2.125 + 1 Reorder the terms: 1 + -2y + y2 = 2.125 + 1 Combine like terms: 2.125 + 1 = 3.125 1 + -2y + y2 = 3.125 Factor a perfect square on the left side: (y + -1)(y + -1) = 3.125 Calculate the square root of the right side: 1.767766953 Break this problem into two subproblems by setting (y + -1) equal to 1.767766953 and -1.767766953.Subproblem 1
y + -1 = 1.767766953 Simplifying y + -1 = 1.767766953 Reorder the terms: -1 + y = 1.767766953 Solving -1 + y = 1.767766953 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = 1.767766953 + 1 Combine like terms: -1 + 1 = 0 0 + y = 1.767766953 + 1 y = 1.767766953 + 1 Combine like terms: 1.767766953 + 1 = 2.767766953 y = 2.767766953 Simplifying y = 2.767766953Subproblem 2
y + -1 = -1.767766953 Simplifying y + -1 = -1.767766953 Reorder the terms: -1 + y = -1.767766953 Solving -1 + y = -1.767766953 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = -1.767766953 + 1 Combine like terms: -1 + 1 = 0 0 + y = -1.767766953 + 1 y = -1.767766953 + 1 Combine like terms: -1.767766953 + 1 = -0.767766953 y = -0.767766953 Simplifying y = -0.767766953Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.767766953, -0.767766953}
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