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Simplifying y2 + 12y = -3 Reorder the terms: 12y + y2 = -3 Solving 12y + y2 = -3 Solving for variable 'y'. Reorder the terms: 3 + 12y + y2 = -3 + 3 Combine like terms: -3 + 3 = 0 3 + 12y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 12y + -3 + y2 = 0 + -3 Reorder the terms: 3 + -3 + 12y + y2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 12y + y2 = 0 + -3 12y + y2 = 0 + -3 Combine like terms: 0 + -3 = -3 12y + y2 = -3 The y term is 12y. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12y + 36 + y2 = -3 + 36 Reorder the terms: 36 + 12y + y2 = -3 + 36 Combine like terms: -3 + 36 = 33 36 + 12y + y2 = 33 Factor a perfect square on the left side: (y + 6)(y + 6) = 33 Calculate the square root of the right side: 5.744562647 Break this problem into two subproblems by setting (y + 6) equal to 5.744562647 and -5.744562647.Subproblem 1
y + 6 = 5.744562647 Simplifying y + 6 = 5.744562647 Reorder the terms: 6 + y = 5.744562647 Solving 6 + y = 5.744562647 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + y = 5.744562647 + -6 Combine like terms: 6 + -6 = 0 0 + y = 5.744562647 + -6 y = 5.744562647 + -6 Combine like terms: 5.744562647 + -6 = -0.255437353 y = -0.255437353 Simplifying y = -0.255437353Subproblem 2
y + 6 = -5.744562647 Simplifying y + 6 = -5.744562647 Reorder the terms: 6 + y = -5.744562647 Solving 6 + y = -5.744562647 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + y = -5.744562647 + -6 Combine like terms: 6 + -6 = 0 0 + y = -5.744562647 + -6 y = -5.744562647 + -6 Combine like terms: -5.744562647 + -6 = -11.744562647 y = -11.744562647 Simplifying y = -11.744562647Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.255437353, -11.744562647}
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