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Simplifying 5y2 + -28y + 9 = 0 Reorder the terms: 9 + -28y + 5y2 = 0 Solving 9 + -28y + 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'. 1.8 + -5.6y + y2 = 0 Move the constant term to the right: Add '-1.8' to each side of the equation. 1.8 + -5.6y + -1.8 + y2 = 0 + -1.8 Reorder the terms: 1.8 + -1.8 + -5.6y + y2 = 0 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + -5.6y + y2 = 0 + -1.8 -5.6y + y2 = 0 + -1.8 Combine like terms: 0 + -1.8 = -1.8 -5.6y + y2 = -1.8 The y term is -5.6y. Take half its coefficient (-2.8). Square it (7.84) and add it to both sides. Add '7.84' to each side of the equation. -5.6y + 7.84 + y2 = -1.8 + 7.84 Reorder the terms: 7.84 + -5.6y + y2 = -1.8 + 7.84 Combine like terms: -1.8 + 7.84 = 6.04 7.84 + -5.6y + y2 = 6.04 Factor a perfect square on the left side: (y + -2.8)(y + -2.8) = 6.04 Calculate the square root of the right side: 2.457641145 Break this problem into two subproblems by setting (y + -2.8) equal to 2.457641145 and -2.457641145.Subproblem 1
y + -2.8 = 2.457641145 Simplifying y + -2.8 = 2.457641145 Reorder the terms: -2.8 + y = 2.457641145 Solving -2.8 + y = 2.457641145 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.8' to each side of the equation. -2.8 + 2.8 + y = 2.457641145 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + y = 2.457641145 + 2.8 y = 2.457641145 + 2.8 Combine like terms: 2.457641145 + 2.8 = 5.257641145 y = 5.257641145 Simplifying y = 5.257641145Subproblem 2
y + -2.8 = -2.457641145 Simplifying y + -2.8 = -2.457641145 Reorder the terms: -2.8 + y = -2.457641145 Solving -2.8 + y = -2.457641145 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.8' to each side of the equation. -2.8 + 2.8 + y = -2.457641145 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + y = -2.457641145 + 2.8 y = -2.457641145 + 2.8 Combine like terms: -2.457641145 + 2.8 = 0.342358855 y = 0.342358855 Simplifying y = 0.342358855Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.257641145, 0.342358855}
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