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Simplifying 10y2 + 60y + 21 = 0 Reorder the terms: 21 + 60y + 10y2 = 0 Solving 21 + 60y + 10y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 2.1 + 6y + y2 = 0 Move the constant term to the right: Add '-2.1' to each side of the equation. 2.1 + 6y + -2.1 + y2 = 0 + -2.1 Reorder the terms: 2.1 + -2.1 + 6y + y2 = 0 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 0.0 + 6y + y2 = 0 + -2.1 6y + y2 = 0 + -2.1 Combine like terms: 0 + -2.1 = -2.1 6y + y2 = -2.1 The y term is 6y. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6y + 9 + y2 = -2.1 + 9 Reorder the terms: 9 + 6y + y2 = -2.1 + 9 Combine like terms: -2.1 + 9 = 6.9 9 + 6y + y2 = 6.9 Factor a perfect square on the left side: (y + 3)(y + 3) = 6.9 Calculate the square root of the right side: 2.626785107 Break this problem into two subproblems by setting (y + 3) equal to 2.626785107 and -2.626785107.Subproblem 1
y + 3 = 2.626785107 Simplifying y + 3 = 2.626785107 Reorder the terms: 3 + y = 2.626785107 Solving 3 + y = 2.626785107 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = 2.626785107 + -3 Combine like terms: 3 + -3 = 0 0 + y = 2.626785107 + -3 y = 2.626785107 + -3 Combine like terms: 2.626785107 + -3 = -0.373214893 y = -0.373214893 Simplifying y = -0.373214893Subproblem 2
y + 3 = -2.626785107 Simplifying y + 3 = -2.626785107 Reorder the terms: 3 + y = -2.626785107 Solving 3 + y = -2.626785107 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = -2.626785107 + -3 Combine like terms: 3 + -3 = 0 0 + y = -2.626785107 + -3 y = -2.626785107 + -3 Combine like terms: -2.626785107 + -3 = -5.626785107 y = -5.626785107 Simplifying y = -5.626785107Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.373214893, -5.626785107}
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