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Simplifying 0 = 2y2 + 24y + 51 Reorder the terms: 0 = 51 + 24y + 2y2 Solving 0 = 51 + 24y + 2y2 Solving for variable 'y'. Combine like terms: 0 + -51 = -51 -51 + -24y + -2y2 = 51 + 24y + 2y2 + -51 + -24y + -2y2 Reorder the terms: -51 + -24y + -2y2 = 51 + -51 + 24y + -24y + 2y2 + -2y2 Combine like terms: 51 + -51 = 0 -51 + -24y + -2y2 = 0 + 24y + -24y + 2y2 + -2y2 -51 + -24y + -2y2 = 24y + -24y + 2y2 + -2y2 Combine like terms: 24y + -24y = 0 -51 + -24y + -2y2 = 0 + 2y2 + -2y2 -51 + -24y + -2y2 = 2y2 + -2y2 Combine like terms: 2y2 + -2y2 = 0 -51 + -24y + -2y2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(51 + 24y + 2y2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(51 + 24y + 2y2)' equal to zero and attempt to solve: Simplifying 51 + 24y + 2y2 = 0 Solving 51 + 24y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 25.5 + 12y + y2 = 0 Move the constant term to the right: Add '-25.5' to each side of the equation. 25.5 + 12y + -25.5 + y2 = 0 + -25.5 Reorder the terms: 25.5 + -25.5 + 12y + y2 = 0 + -25.5 Combine like terms: 25.5 + -25.5 = 0.0 0.0 + 12y + y2 = 0 + -25.5 12y + y2 = 0 + -25.5 Combine like terms: 0 + -25.5 = -25.5 12y + y2 = -25.5 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 = -25.5 + 36 Reorder the terms: 36 + 12y + y2 = -25.5 + 36 Combine like terms: -25.5 + 36 = 10.5 36 + 12y + y2 = 10.5 Factor a perfect square on the left side: (y + 6)(y + 6) = 10.5 Calculate the square root of the right side: 3.240370349 Break this problem into two subproblems by setting (y + 6) equal to 3.240370349 and -3.240370349.Subproblem 1
y + 6 = 3.240370349 Simplifying y + 6 = 3.240370349 Reorder the terms: 6 + y = 3.240370349 Solving 6 + y = 3.240370349 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 = 3.240370349 + -6 Combine like terms: 6 + -6 = 0 0 + y = 3.240370349 + -6 y = 3.240370349 + -6 Combine like terms: 3.240370349 + -6 = -2.759629651 y = -2.759629651 Simplifying y = -2.759629651Subproblem 2
y + 6 = -3.240370349 Simplifying y + 6 = -3.240370349 Reorder the terms: 6 + y = -3.240370349 Solving 6 + y = -3.240370349 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 = -3.240370349 + -6 Combine like terms: 6 + -6 = 0 0 + y = -3.240370349 + -6 y = -3.240370349 + -6 Combine like terms: -3.240370349 + -6 = -9.240370349 y = -9.240370349 Simplifying y = -9.240370349Solution
The solution to the problem is based on the solutions from the subproblems. y = {-2.759629651, -9.240370349}Solution
y = {-2.759629651, -9.240370349}
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