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Simplifying y2 + -12y + 3 = 5 Reorder the terms: 3 + -12y + y2 = 5 Solving 3 + -12y + y2 = 5 Solving for variable 'y'. Reorder the terms: 3 + -5 + -12y + y2 = 5 + -5 Combine like terms: 3 + -5 = -2 -2 + -12y + y2 = 5 + -5 Combine like terms: 5 + -5 = 0 -2 + -12y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -12y + 2 + y2 = 0 + 2 Reorder the terms: -2 + 2 + -12y + y2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -12y + y2 = 0 + 2 -12y + y2 = 0 + 2 Combine like terms: 0 + 2 = 2 -12y + y2 = 2 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 = 2 + 36 Reorder the terms: 36 + -12y + y2 = 2 + 36 Combine like terms: 2 + 36 = 38 36 + -12y + y2 = 38 Factor a perfect square on the left side: (y + -6)(y + -6) = 38 Calculate the square root of the right side: 6.164414003 Break this problem into two subproblems by setting (y + -6) equal to 6.164414003 and -6.164414003.Subproblem 1
y + -6 = 6.164414003 Simplifying y + -6 = 6.164414003 Reorder the terms: -6 + y = 6.164414003 Solving -6 + y = 6.164414003 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 = 6.164414003 + 6 Combine like terms: -6 + 6 = 0 0 + y = 6.164414003 + 6 y = 6.164414003 + 6 Combine like terms: 6.164414003 + 6 = 12.164414003 y = 12.164414003 Simplifying y = 12.164414003Subproblem 2
y + -6 = -6.164414003 Simplifying y + -6 = -6.164414003 Reorder the terms: -6 + y = -6.164414003 Solving -6 + y = -6.164414003 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 = -6.164414003 + 6 Combine like terms: -6 + 6 = 0 0 + y = -6.164414003 + 6 y = -6.164414003 + 6 Combine like terms: -6.164414003 + 6 = -0.164414003 y = -0.164414003 Simplifying y = -0.164414003Solution
The solution to the problem is based on the solutions from the subproblems. y = {12.164414003, -0.164414003}
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