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Simplifying 24y2 + -11y + -14 = 0 Reorder the terms: -14 + -11y + 24y2 = 0 Solving -14 + -11y + 24y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -0.5833333333 + -0.4583333333y + y2 = 0 Move the constant term to the right: Add '0.5833333333' to each side of the equation. -0.5833333333 + -0.4583333333y + 0.5833333333 + y2 = 0 + 0.5833333333 Reorder the terms: -0.5833333333 + 0.5833333333 + -0.4583333333y + y2 = 0 + 0.5833333333 Combine like terms: -0.5833333333 + 0.5833333333 = 0.0000000000 0.0000000000 + -0.4583333333y + y2 = 0 + 0.5833333333 -0.4583333333y + y2 = 0 + 0.5833333333 Combine like terms: 0 + 0.5833333333 = 0.5833333333 -0.4583333333y + y2 = 0.5833333333 The y term is -0.4583333333y. Take half its coefficient (-0.2291666667). Square it (0.05251736113) and add it to both sides. Add '0.05251736113' to each side of the equation. -0.4583333333y + 0.05251736113 + y2 = 0.5833333333 + 0.05251736113 Reorder the terms: 0.05251736113 + -0.4583333333y + y2 = 0.5833333333 + 0.05251736113 Combine like terms: 0.5833333333 + 0.05251736113 = 0.63585069443 0.05251736113 + -0.4583333333y + y2 = 0.63585069443 Factor a perfect square on the left side: (y + -0.2291666667)(y + -0.2291666667) = 0.63585069443 Calculate the square root of the right side: 0.797402467 Break this problem into two subproblems by setting (y + -0.2291666667) equal to 0.797402467 and -0.797402467.Subproblem 1
y + -0.2291666667 = 0.797402467 Simplifying y + -0.2291666667 = 0.797402467 Reorder the terms: -0.2291666667 + y = 0.797402467 Solving -0.2291666667 + y = 0.797402467 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.2291666667' to each side of the equation. -0.2291666667 + 0.2291666667 + y = 0.797402467 + 0.2291666667 Combine like terms: -0.2291666667 + 0.2291666667 = 0.0000000000 0.0000000000 + y = 0.797402467 + 0.2291666667 y = 0.797402467 + 0.2291666667 Combine like terms: 0.797402467 + 0.2291666667 = 1.0265691337 y = 1.0265691337 Simplifying y = 1.0265691337Subproblem 2
y + -0.2291666667 = -0.797402467 Simplifying y + -0.2291666667 = -0.797402467 Reorder the terms: -0.2291666667 + y = -0.797402467 Solving -0.2291666667 + y = -0.797402467 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.2291666667' to each side of the equation. -0.2291666667 + 0.2291666667 + y = -0.797402467 + 0.2291666667 Combine like terms: -0.2291666667 + 0.2291666667 = 0.0000000000 0.0000000000 + y = -0.797402467 + 0.2291666667 y = -0.797402467 + 0.2291666667 Combine like terms: -0.797402467 + 0.2291666667 = -0.5682358003 y = -0.5682358003 Simplifying y = -0.5682358003Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.0265691337, -0.5682358003}
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