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Simplifying 6y2 + -24y + 9 = 0 Reorder the terms: 9 + -24y + 6y2 = 0 Solving 9 + -24y + 6y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '3'. 3(3 + -8y + 2y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + -8y + 2y2)' equal to zero and attempt to solve: Simplifying 3 + -8y + 2y2 = 0 Solving 3 + -8y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + -4y + y2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -4y + -1.5 + y2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -4y + y2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -4y + y2 = 0 + -1.5 -4y + y2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -4y + y2 = -1.5 The y term is -4y. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4y + 4 + y2 = -1.5 + 4 Reorder the terms: 4 + -4y + y2 = -1.5 + 4 Combine like terms: -1.5 + 4 = 2.5 4 + -4y + y2 = 2.5 Factor a perfect square on the left side: (y + -2)(y + -2) = 2.5 Calculate the square root of the right side: 1.58113883 Break this problem into two subproblems by setting (y + -2) equal to 1.58113883 and -1.58113883.Subproblem 1
y + -2 = 1.58113883 Simplifying y + -2 = 1.58113883 Reorder the terms: -2 + y = 1.58113883 Solving -2 + y = 1.58113883 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = 1.58113883 + 2 Combine like terms: -2 + 2 = 0 0 + y = 1.58113883 + 2 y = 1.58113883 + 2 Combine like terms: 1.58113883 + 2 = 3.58113883 y = 3.58113883 Simplifying y = 3.58113883Subproblem 2
y + -2 = -1.58113883 Simplifying y + -2 = -1.58113883 Reorder the terms: -2 + y = -1.58113883 Solving -2 + y = -1.58113883 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = -1.58113883 + 2 Combine like terms: -2 + 2 = 0 0 + y = -1.58113883 + 2 y = -1.58113883 + 2 Combine like terms: -1.58113883 + 2 = 0.41886117 y = 0.41886117 Simplifying y = 0.41886117Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.58113883, 0.41886117}Solution
y = {3.58113883, 0.41886117}
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