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Simplifying (5y + -1)(y + -1) = 50 Reorder the terms: (-1 + 5y)(y + -1) = 50 Reorder the terms: (-1 + 5y)(-1 + y) = 50 Multiply (-1 + 5y) * (-1 + y) (-1(-1 + y) + 5y * (-1 + y)) = 50 ((-1 * -1 + y * -1) + 5y * (-1 + y)) = 50 ((1 + -1y) + 5y * (-1 + y)) = 50 (1 + -1y + (-1 * 5y + y * 5y)) = 50 (1 + -1y + (-5y + 5y2)) = 50 Combine like terms: -1y + -5y = -6y (1 + -6y + 5y2) = 50 Solving 1 + -6y + 5y2 = 50 Solving for variable 'y'. Reorder the terms: 1 + -50 + -6y + 5y2 = 50 + -50 Combine like terms: 1 + -50 = -49 -49 + -6y + 5y2 = 50 + -50 Combine like terms: 50 + -50 = 0 -49 + -6y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -9.8 + -1.2y + y2 = 0 Move the constant term to the right: Add '9.8' to each side of the equation. -9.8 + -1.2y + 9.8 + y2 = 0 + 9.8 Reorder the terms: -9.8 + 9.8 + -1.2y + y2 = 0 + 9.8 Combine like terms: -9.8 + 9.8 = 0.0 0.0 + -1.2y + y2 = 0 + 9.8 -1.2y + y2 = 0 + 9.8 Combine like terms: 0 + 9.8 = 9.8 -1.2y + y2 = 9.8 The y term is -1.2y. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2y + 0.36 + y2 = 9.8 + 0.36 Reorder the terms: 0.36 + -1.2y + y2 = 9.8 + 0.36 Combine like terms: 9.8 + 0.36 = 10.16 0.36 + -1.2y + y2 = 10.16 Factor a perfect square on the left side: (y + -0.6)(y + -0.6) = 10.16 Calculate the square root of the right side: 3.18747549 Break this problem into two subproblems by setting (y + -0.6) equal to 3.18747549 and -3.18747549.Subproblem 1
y + -0.6 = 3.18747549 Simplifying y + -0.6 = 3.18747549 Reorder the terms: -0.6 + y = 3.18747549 Solving -0.6 + y = 3.18747549 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + y = 3.18747549 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + y = 3.18747549 + 0.6 y = 3.18747549 + 0.6 Combine like terms: 3.18747549 + 0.6 = 3.78747549 y = 3.78747549 Simplifying y = 3.78747549Subproblem 2
y + -0.6 = -3.18747549 Simplifying y + -0.6 = -3.18747549 Reorder the terms: -0.6 + y = -3.18747549 Solving -0.6 + y = -3.18747549 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + y = -3.18747549 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + y = -3.18747549 + 0.6 y = -3.18747549 + 0.6 Combine like terms: -3.18747549 + 0.6 = -2.58747549 y = -2.58747549 Simplifying y = -2.58747549Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.78747549, -2.58747549}
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