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Simplifying 24y2 + 28y + -24 = 0 Reorder the terms: -24 + 28y + 24y2 = 0 Solving -24 + 28y + 24y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '4'. 4(-6 + 7y + 6y2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-6 + 7y + 6y2)' equal to zero and attempt to solve: Simplifying -6 + 7y + 6y2 = 0 Solving -6 + 7y + 6y2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1 + 1.166666667y + y2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 1.166666667y + 1 + y2 = 0 + 1 Reorder the terms: -1 + 1 + 1.166666667y + y2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 1.166666667y + y2 = 0 + 1 1.166666667y + y2 = 0 + 1 Combine like terms: 0 + 1 = 1 1.166666667y + y2 = 1 The y term is 1.166666667y. Take half its coefficient (0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. 1.166666667y + 0.3402777780 + y2 = 1 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667y + y2 = 1 + 0.3402777780 Combine like terms: 1 + 0.3402777780 = 1.340277778 0.3402777780 + 1.166666667y + y2 = 1.340277778 Factor a perfect square on the left side: (y + 0.5833333335)(y + 0.5833333335) = 1.340277778 Calculate the square root of the right side: 1.157703666 Break this problem into two subproblems by setting (y + 0.5833333335) equal to 1.157703666 and -1.157703666.Subproblem 1
y + 0.5833333335 = 1.157703666 Simplifying y + 0.5833333335 = 1.157703666 Reorder the terms: 0.5833333335 + y = 1.157703666 Solving 0.5833333335 + y = 1.157703666 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + y = 1.157703666 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + y = 1.157703666 + -0.5833333335 y = 1.157703666 + -0.5833333335 Combine like terms: 1.157703666 + -0.5833333335 = 0.5743703325 y = 0.5743703325 Simplifying y = 0.5743703325Subproblem 2
y + 0.5833333335 = -1.157703666 Simplifying y + 0.5833333335 = -1.157703666 Reorder the terms: 0.5833333335 + y = -1.157703666 Solving 0.5833333335 + y = -1.157703666 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + y = -1.157703666 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + y = -1.157703666 + -0.5833333335 y = -1.157703666 + -0.5833333335 Combine like terms: -1.157703666 + -0.5833333335 = -1.7410369995 y = -1.7410369995 Simplifying y = -1.7410369995Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.5743703325, -1.7410369995}Solution
y = {0.5743703325, -1.7410369995}
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