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Simplifying 3y2 + 6y + -42 = 0 Reorder the terms: -42 + 6y + 3y2 = 0 Solving -42 + 6y + 3y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '3'. 3(-14 + 2y + y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-14 + 2y + y2)' equal to zero and attempt to solve: Simplifying -14 + 2y + y2 = 0 Solving -14 + 2y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + 2y + 14 + y2 = 0 + 14 Reorder the terms: -14 + 14 + 2y + y2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 2y + y2 = 0 + 14 2y + y2 = 0 + 14 Combine like terms: 0 + 14 = 14 2y + y2 = 14 The y term is 2y. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2y + 1 + y2 = 14 + 1 Reorder the terms: 1 + 2y + y2 = 14 + 1 Combine like terms: 14 + 1 = 15 1 + 2y + y2 = 15 Factor a perfect square on the left side: (y + 1)(y + 1) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (y + 1) equal to 3.872983346 and -3.872983346.Subproblem 1
y + 1 = 3.872983346 Simplifying y + 1 = 3.872983346 Reorder the terms: 1 + y = 3.872983346 Solving 1 + y = 3.872983346 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = 3.872983346 + -1 Combine like terms: 1 + -1 = 0 0 + y = 3.872983346 + -1 y = 3.872983346 + -1 Combine like terms: 3.872983346 + -1 = 2.872983346 y = 2.872983346 Simplifying y = 2.872983346Subproblem 2
y + 1 = -3.872983346 Simplifying y + 1 = -3.872983346 Reorder the terms: 1 + y = -3.872983346 Solving 1 + y = -3.872983346 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = -3.872983346 + -1 Combine like terms: 1 + -1 = 0 0 + y = -3.872983346 + -1 y = -3.872983346 + -1 Combine like terms: -3.872983346 + -1 = -4.872983346 y = -4.872983346 Simplifying y = -4.872983346Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.872983346, -4.872983346}Solution
y = {2.872983346, -4.872983346}
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