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Simplifying 5(y2 + -6y + -9) = 0 Reorder the terms: 5(-9 + -6y + y2) = 0 (-9 * 5 + -6y * 5 + y2 * 5) = 0 (-45 + -30y + 5y2) = 0 Solving -45 + -30y + 5y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '5'. 5(-9 + -6y + y2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-9 + -6y + y2)' equal to zero and attempt to solve: Simplifying -9 + -6y + y2 = 0 Solving -9 + -6y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -6y + 9 + y2 = 0 + 9 Reorder the terms: -9 + 9 + -6y + y2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -6y + y2 = 0 + 9 -6y + y2 = 0 + 9 Combine like terms: 0 + 9 = 9 -6y + y2 = 9 The y term is -6y. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6y + 9 + y2 = 9 + 9 Reorder the terms: 9 + -6y + y2 = 9 + 9 Combine like terms: 9 + 9 = 18 9 + -6y + y2 = 18 Factor a perfect square on the left side: (y + -3)(y + -3) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (y + -3) equal to 4.242640687 and -4.242640687.Subproblem 1
y + -3 = 4.242640687 Simplifying y + -3 = 4.242640687 Reorder the terms: -3 + y = 4.242640687 Solving -3 + y = 4.242640687 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = 4.242640687 + 3 Combine like terms: -3 + 3 = 0 0 + y = 4.242640687 + 3 y = 4.242640687 + 3 Combine like terms: 4.242640687 + 3 = 7.242640687 y = 7.242640687 Simplifying y = 7.242640687Subproblem 2
y + -3 = -4.242640687 Simplifying y + -3 = -4.242640687 Reorder the terms: -3 + y = -4.242640687 Solving -3 + y = -4.242640687 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = -4.242640687 + 3 Combine like terms: -3 + 3 = 0 0 + y = -4.242640687 + 3 y = -4.242640687 + 3 Combine like terms: -4.242640687 + 3 = -1.242640687 y = -1.242640687 Simplifying y = -1.242640687Solution
The solution to the problem is based on the solutions from the subproblems. y = {7.242640687, -1.242640687}Solution
y = {7.242640687, -1.242640687}
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