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Simplifying 5y2 + -8y = 27 Reorder the terms: -8y + 5y2 = 27 Solving -8y + 5y2 = 27 Solving for variable 'y'. Reorder the terms: -27 + -8y + 5y2 = 27 + -27 Combine like terms: 27 + -27 = 0 -27 + -8y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5.4 + -1.6y + y2 = 0 Move the constant term to the right: Add '5.4' to each side of the equation. -5.4 + -1.6y + 5.4 + y2 = 0 + 5.4 Reorder the terms: -5.4 + 5.4 + -1.6y + y2 = 0 + 5.4 Combine like terms: -5.4 + 5.4 = 0.0 0.0 + -1.6y + y2 = 0 + 5.4 -1.6y + y2 = 0 + 5.4 Combine like terms: 0 + 5.4 = 5.4 -1.6y + y2 = 5.4 The y term is -1.6y. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6y + 0.64 + y2 = 5.4 + 0.64 Reorder the terms: 0.64 + -1.6y + y2 = 5.4 + 0.64 Combine like terms: 5.4 + 0.64 = 6.04 0.64 + -1.6y + y2 = 6.04 Factor a perfect square on the left side: (y + -0.8)(y + -0.8) = 6.04 Calculate the square root of the right side: 2.457641145 Break this problem into two subproblems by setting (y + -0.8) equal to 2.457641145 and -2.457641145.Subproblem 1
y + -0.8 = 2.457641145 Simplifying y + -0.8 = 2.457641145 Reorder the terms: -0.8 + y = 2.457641145 Solving -0.8 + y = 2.457641145 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + y = 2.457641145 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + y = 2.457641145 + 0.8 y = 2.457641145 + 0.8 Combine like terms: 2.457641145 + 0.8 = 3.257641145 y = 3.257641145 Simplifying y = 3.257641145Subproblem 2
y + -0.8 = -2.457641145 Simplifying y + -0.8 = -2.457641145 Reorder the terms: -0.8 + y = -2.457641145 Solving -0.8 + y = -2.457641145 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + y = -2.457641145 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + y = -2.457641145 + 0.8 y = -2.457641145 + 0.8 Combine like terms: -2.457641145 + 0.8 = -1.657641145 y = -1.657641145 Simplifying y = -1.657641145Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.257641145, -1.657641145}
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