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Simplifying 6y2 + 84y + -36 = 0 Reorder the terms: -36 + 84y + 6y2 = 0 Solving -36 + 84y + 6y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '6'. 6(-6 + 14y + y2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-6 + 14y + y2)' equal to zero and attempt to solve: Simplifying -6 + 14y + y2 = 0 Solving -6 + 14y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 14y + 6 + y2 = 0 + 6 Reorder the terms: -6 + 6 + 14y + y2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 14y + y2 = 0 + 6 14y + y2 = 0 + 6 Combine like terms: 0 + 6 = 6 14y + y2 = 6 The y term is 14y. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14y + 49 + y2 = 6 + 49 Reorder the terms: 49 + 14y + y2 = 6 + 49 Combine like terms: 6 + 49 = 55 49 + 14y + y2 = 55 Factor a perfect square on the left side: (y + 7)(y + 7) = 55 Calculate the square root of the right side: 7.416198487 Break this problem into two subproblems by setting (y + 7) equal to 7.416198487 and -7.416198487.Subproblem 1
y + 7 = 7.416198487 Simplifying y + 7 = 7.416198487 Reorder the terms: 7 + y = 7.416198487 Solving 7 + y = 7.416198487 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + y = 7.416198487 + -7 Combine like terms: 7 + -7 = 0 0 + y = 7.416198487 + -7 y = 7.416198487 + -7 Combine like terms: 7.416198487 + -7 = 0.416198487 y = 0.416198487 Simplifying y = 0.416198487Subproblem 2
y + 7 = -7.416198487 Simplifying y + 7 = -7.416198487 Reorder the terms: 7 + y = -7.416198487 Solving 7 + y = -7.416198487 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + y = -7.416198487 + -7 Combine like terms: 7 + -7 = 0 0 + y = -7.416198487 + -7 y = -7.416198487 + -7 Combine like terms: -7.416198487 + -7 = -14.416198487 y = -14.416198487 Simplifying y = -14.416198487Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.416198487, -14.416198487}Solution
y = {0.416198487, -14.416198487}
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