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Simplifying 2y2 + 9y + -2 = (y + 2)(y + -7) Reorder the terms: -2 + 9y + 2y2 = (y + 2)(y + -7) Reorder the terms: -2 + 9y + 2y2 = (2 + y)(y + -7) Reorder the terms: -2 + 9y + 2y2 = (2 + y)(-7 + y) Multiply (2 + y) * (-7 + y) -2 + 9y + 2y2 = (2(-7 + y) + y(-7 + y)) -2 + 9y + 2y2 = ((-7 * 2 + y * 2) + y(-7 + y)) -2 + 9y + 2y2 = ((-14 + 2y) + y(-7 + y)) -2 + 9y + 2y2 = (-14 + 2y + (-7 * y + y * y)) -2 + 9y + 2y2 = (-14 + 2y + (-7y + y2)) Combine like terms: 2y + -7y = -5y -2 + 9y + 2y2 = (-14 + -5y + y2) Solving -2 + 9y + 2y2 = -14 + -5y + y2 Solving for variable 'y'. Reorder the terms: -2 + 14 + 9y + 5y + 2y2 + -1y2 = -14 + -5y + y2 + 14 + 5y + -1y2 Combine like terms: -2 + 14 = 12 12 + 9y + 5y + 2y2 + -1y2 = -14 + -5y + y2 + 14 + 5y + -1y2 Combine like terms: 9y + 5y = 14y 12 + 14y + 2y2 + -1y2 = -14 + -5y + y2 + 14 + 5y + -1y2 Combine like terms: 2y2 + -1y2 = 1y2 12 + 14y + 1y2 = -14 + -5y + y2 + 14 + 5y + -1y2 Reorder the terms: 12 + 14y + 1y2 = -14 + 14 + -5y + 5y + y2 + -1y2 Combine like terms: -14 + 14 = 0 12 + 14y + 1y2 = 0 + -5y + 5y + y2 + -1y2 12 + 14y + 1y2 = -5y + 5y + y2 + -1y2 Combine like terms: -5y + 5y = 0 12 + 14y + 1y2 = 0 + y2 + -1y2 12 + 14y + 1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 12 + 14y + 1y2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + 14y + -12 + y2 = 0 + -12 Reorder the terms: 12 + -12 + 14y + y2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 14y + y2 = 0 + -12 14y + y2 = 0 + -12 Combine like terms: 0 + -12 = -12 14y + y2 = -12 The y term is 14y. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14y + 49 + y2 = -12 + 49 Reorder the terms: 49 + 14y + y2 = -12 + 49 Combine like terms: -12 + 49 = 37 49 + 14y + y2 = 37 Factor a perfect square on the left side: (y + 7)(y + 7) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (y + 7) equal to 6.08276253 and -6.08276253.Subproblem 1
y + 7 = 6.08276253 Simplifying y + 7 = 6.08276253 Reorder the terms: 7 + y = 6.08276253 Solving 7 + y = 6.08276253 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + y = 6.08276253 + -7 Combine like terms: 7 + -7 = 0 0 + y = 6.08276253 + -7 y = 6.08276253 + -7 Combine like terms: 6.08276253 + -7 = -0.91723747 y = -0.91723747 Simplifying y = -0.91723747Subproblem 2
y + 7 = -6.08276253 Simplifying y + 7 = -6.08276253 Reorder the terms: 7 + y = -6.08276253 Solving 7 + y = -6.08276253 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + y = -6.08276253 + -7 Combine like terms: 7 + -7 = 0 0 + y = -6.08276253 + -7 y = -6.08276253 + -7 Combine like terms: -6.08276253 + -7 = -13.08276253 y = -13.08276253 Simplifying y = -13.08276253Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.91723747, -13.08276253}
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