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Simplifying 3y2 + 12y + -32 = 0 Reorder the terms: -32 + 12y + 3y2 = 0 Solving -32 + 12y + 3y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -10.66666667 + 4y + y2 = 0 Move the constant term to the right: Add '10.66666667' to each side of the equation. -10.66666667 + 4y + 10.66666667 + y2 = 0 + 10.66666667 Reorder the terms: -10.66666667 + 10.66666667 + 4y + y2 = 0 + 10.66666667 Combine like terms: -10.66666667 + 10.66666667 = 0.00000000 0.00000000 + 4y + y2 = 0 + 10.66666667 4y + y2 = 0 + 10.66666667 Combine like terms: 0 + 10.66666667 = 10.66666667 4y + y2 = 10.66666667 The y term is 4y. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4y + 4 + y2 = 10.66666667 + 4 Reorder the terms: 4 + 4y + y2 = 10.66666667 + 4 Combine like terms: 10.66666667 + 4 = 14.66666667 4 + 4y + y2 = 14.66666667 Factor a perfect square on the left side: (y + 2)(y + 2) = 14.66666667 Calculate the square root of the right side: 3.829708431 Break this problem into two subproblems by setting (y + 2) equal to 3.829708431 and -3.829708431.Subproblem 1
y + 2 = 3.829708431 Simplifying y + 2 = 3.829708431 Reorder the terms: 2 + y = 3.829708431 Solving 2 + y = 3.829708431 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = 3.829708431 + -2 Combine like terms: 2 + -2 = 0 0 + y = 3.829708431 + -2 y = 3.829708431 + -2 Combine like terms: 3.829708431 + -2 = 1.829708431 y = 1.829708431 Simplifying y = 1.829708431Subproblem 2
y + 2 = -3.829708431 Simplifying y + 2 = -3.829708431 Reorder the terms: 2 + y = -3.829708431 Solving 2 + y = -3.829708431 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = -3.829708431 + -2 Combine like terms: 2 + -2 = 0 0 + y = -3.829708431 + -2 y = -3.829708431 + -2 Combine like terms: -3.829708431 + -2 = -5.829708431 y = -5.829708431 Simplifying y = -5.829708431Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.829708431, -5.829708431}
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