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Simplifying 5y2 + -24y + -8 = 0 Reorder the terms: -8 + -24y + 5y2 = 0 Solving -8 + -24y + 5y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.6 + -4.8y + y2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + -4.8y + 1.6 + y2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + -4.8y + y2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + -4.8y + y2 = 0 + 1.6 -4.8y + y2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 -4.8y + y2 = 1.6 The y term is -4.8y. Take half its coefficient (-2.4). Square it (5.76) and add it to both sides. Add '5.76' to each side of the equation. -4.8y + 5.76 + y2 = 1.6 + 5.76 Reorder the terms: 5.76 + -4.8y + y2 = 1.6 + 5.76 Combine like terms: 1.6 + 5.76 = 7.36 5.76 + -4.8y + y2 = 7.36 Factor a perfect square on the left side: (y + -2.4)(y + -2.4) = 7.36 Calculate the square root of the right side: 2.712931993 Break this problem into two subproblems by setting (y + -2.4) equal to 2.712931993 and -2.712931993.Subproblem 1
y + -2.4 = 2.712931993 Simplifying y + -2.4 = 2.712931993 Reorder the terms: -2.4 + y = 2.712931993 Solving -2.4 + y = 2.712931993 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + y = 2.712931993 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + y = 2.712931993 + 2.4 y = 2.712931993 + 2.4 Combine like terms: 2.712931993 + 2.4 = 5.112931993 y = 5.112931993 Simplifying y = 5.112931993Subproblem 2
y + -2.4 = -2.712931993 Simplifying y + -2.4 = -2.712931993 Reorder the terms: -2.4 + y = -2.712931993 Solving -2.4 + y = -2.712931993 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + y = -2.712931993 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + y = -2.712931993 + 2.4 y = -2.712931993 + 2.4 Combine like terms: -2.712931993 + 2.4 = -0.312931993 y = -0.312931993 Simplifying y = -0.312931993Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.112931993, -0.312931993}
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