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Simplifying 5y2 + -33y + -54 = 0 Reorder the terms: -54 + -33y + 5y2 = 0 Solving -54 + -33y + 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'. -10.8 + -6.6y + y2 = 0 Move the constant term to the right: Add '10.8' to each side of the equation. -10.8 + -6.6y + 10.8 + y2 = 0 + 10.8 Reorder the terms: -10.8 + 10.8 + -6.6y + y2 = 0 + 10.8 Combine like terms: -10.8 + 10.8 = 0.0 0.0 + -6.6y + y2 = 0 + 10.8 -6.6y + y2 = 0 + 10.8 Combine like terms: 0 + 10.8 = 10.8 -6.6y + y2 = 10.8 The y term is -6.6y. Take half its coefficient (-3.3). Square it (10.89) and add it to both sides. Add '10.89' to each side of the equation. -6.6y + 10.89 + y2 = 10.8 + 10.89 Reorder the terms: 10.89 + -6.6y + y2 = 10.8 + 10.89 Combine like terms: 10.8 + 10.89 = 21.69 10.89 + -6.6y + y2 = 21.69 Factor a perfect square on the left side: (y + -3.3)(y + -3.3) = 21.69 Calculate the square root of the right side: 4.657252409 Break this problem into two subproblems by setting (y + -3.3) equal to 4.657252409 and -4.657252409.Subproblem 1
y + -3.3 = 4.657252409 Simplifying y + -3.3 = 4.657252409 Reorder the terms: -3.3 + y = 4.657252409 Solving -3.3 + y = 4.657252409 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.3' to each side of the equation. -3.3 + 3.3 + y = 4.657252409 + 3.3 Combine like terms: -3.3 + 3.3 = 0.0 0.0 + y = 4.657252409 + 3.3 y = 4.657252409 + 3.3 Combine like terms: 4.657252409 + 3.3 = 7.957252409 y = 7.957252409 Simplifying y = 7.957252409Subproblem 2
y + -3.3 = -4.657252409 Simplifying y + -3.3 = -4.657252409 Reorder the terms: -3.3 + y = -4.657252409 Solving -3.3 + y = -4.657252409 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.3' to each side of the equation. -3.3 + 3.3 + y = -4.657252409 + 3.3 Combine like terms: -3.3 + 3.3 = 0.0 0.0 + y = -4.657252409 + 3.3 y = -4.657252409 + 3.3 Combine like terms: -4.657252409 + 3.3 = -1.357252409 y = -1.357252409 Simplifying y = -1.357252409Solution
The solution to the problem is based on the solutions from the subproblems. y = {7.957252409, -1.357252409}
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