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Simplifying 6y2 + -21y + -7 = 0 Reorder the terms: -7 + -21y + 6y2 = 0 Solving -7 + -21y + 6y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.166666667 + -3.5y + y2 = 0 Move the constant term to the right: Add '1.166666667' to each side of the equation. -1.166666667 + -3.5y + 1.166666667 + y2 = 0 + 1.166666667 Reorder the terms: -1.166666667 + 1.166666667 + -3.5y + y2 = 0 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + -3.5y + y2 = 0 + 1.166666667 -3.5y + y2 = 0 + 1.166666667 Combine like terms: 0 + 1.166666667 = 1.166666667 -3.5y + y2 = 1.166666667 The y term is -3.5y. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5y + 3.0625 + y2 = 1.166666667 + 3.0625 Reorder the terms: 3.0625 + -3.5y + y2 = 1.166666667 + 3.0625 Combine like terms: 1.166666667 + 3.0625 = 4.229166667 3.0625 + -3.5y + y2 = 4.229166667 Factor a perfect square on the left side: (y + -1.75)(y + -1.75) = 4.229166667 Calculate the square root of the right side: 2.05649378 Break this problem into two subproblems by setting (y + -1.75) equal to 2.05649378 and -2.05649378.Subproblem 1
y + -1.75 = 2.05649378 Simplifying y + -1.75 = 2.05649378 Reorder the terms: -1.75 + y = 2.05649378 Solving -1.75 + y = 2.05649378 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + y = 2.05649378 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + y = 2.05649378 + 1.75 y = 2.05649378 + 1.75 Combine like terms: 2.05649378 + 1.75 = 3.80649378 y = 3.80649378 Simplifying y = 3.80649378Subproblem 2
y + -1.75 = -2.05649378 Simplifying y + -1.75 = -2.05649378 Reorder the terms: -1.75 + y = -2.05649378 Solving -1.75 + y = -2.05649378 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + y = -2.05649378 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + y = -2.05649378 + 1.75 y = -2.05649378 + 1.75 Combine like terms: -2.05649378 + 1.75 = -0.30649378 y = -0.30649378 Simplifying y = -0.30649378Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.80649378, -0.30649378}
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