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Simplifying 5y2 + -44y + -96 = 0 Reorder the terms: -96 + -44y + 5y2 = 0 Solving -96 + -44y + 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'. -19.2 + -8.8y + y2 = 0 Move the constant term to the right: Add '19.2' to each side of the equation. -19.2 + -8.8y + 19.2 + y2 = 0 + 19.2 Reorder the terms: -19.2 + 19.2 + -8.8y + y2 = 0 + 19.2 Combine like terms: -19.2 + 19.2 = 0.0 0.0 + -8.8y + y2 = 0 + 19.2 -8.8y + y2 = 0 + 19.2 Combine like terms: 0 + 19.2 = 19.2 -8.8y + y2 = 19.2 The y term is -8.8y. Take half its coefficient (-4.4). Square it (19.36) and add it to both sides. Add '19.36' to each side of the equation. -8.8y + 19.36 + y2 = 19.2 + 19.36 Reorder the terms: 19.36 + -8.8y + y2 = 19.2 + 19.36 Combine like terms: 19.2 + 19.36 = 38.56 19.36 + -8.8y + y2 = 38.56 Factor a perfect square on the left side: (y + -4.4)(y + -4.4) = 38.56 Calculate the square root of the right side: 6.209669879 Break this problem into two subproblems by setting (y + -4.4) equal to 6.209669879 and -6.209669879.Subproblem 1
y + -4.4 = 6.209669879 Simplifying y + -4.4 = 6.209669879 Reorder the terms: -4.4 + y = 6.209669879 Solving -4.4 + y = 6.209669879 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.4' to each side of the equation. -4.4 + 4.4 + y = 6.209669879 + 4.4 Combine like terms: -4.4 + 4.4 = 0.0 0.0 + y = 6.209669879 + 4.4 y = 6.209669879 + 4.4 Combine like terms: 6.209669879 + 4.4 = 10.609669879 y = 10.609669879 Simplifying y = 10.609669879Subproblem 2
y + -4.4 = -6.209669879 Simplifying y + -4.4 = -6.209669879 Reorder the terms: -4.4 + y = -6.209669879 Solving -4.4 + y = -6.209669879 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.4' to each side of the equation. -4.4 + 4.4 + y = -6.209669879 + 4.4 Combine like terms: -4.4 + 4.4 = 0.0 0.0 + y = -6.209669879 + 4.4 y = -6.209669879 + 4.4 Combine like terms: -6.209669879 + 4.4 = -1.809669879 y = -1.809669879 Simplifying y = -1.809669879Solution
The solution to the problem is based on the solutions from the subproblems. y = {10.609669879, -1.809669879}
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