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Simplifying 5y2 + -28y + -15 = 0 Reorder the terms: -15 + -28y + 5y2 = 0 Solving -15 + -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'. -3 + -5.6y + y2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -5.6y + 3 + y2 = 0 + 3 Reorder the terms: -3 + 3 + -5.6y + y2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5.6y + y2 = 0 + 3 -5.6y + y2 = 0 + 3 Combine like terms: 0 + 3 = 3 -5.6y + y2 = 3 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 = 3 + 7.84 Reorder the terms: 7.84 + -5.6y + y2 = 3 + 7.84 Combine like terms: 3 + 7.84 = 10.84 7.84 + -5.6y + y2 = 10.84 Factor a perfect square on the left side: (y + -2.8)(y + -2.8) = 10.84 Calculate the square root of the right side: 3.292415527 Break this problem into two subproblems by setting (y + -2.8) equal to 3.292415527 and -3.292415527.Subproblem 1
y + -2.8 = 3.292415527 Simplifying y + -2.8 = 3.292415527 Reorder the terms: -2.8 + y = 3.292415527 Solving -2.8 + y = 3.292415527 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 = 3.292415527 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + y = 3.292415527 + 2.8 y = 3.292415527 + 2.8 Combine like terms: 3.292415527 + 2.8 = 6.092415527 y = 6.092415527 Simplifying y = 6.092415527Subproblem 2
y + -2.8 = -3.292415527 Simplifying y + -2.8 = -3.292415527 Reorder the terms: -2.8 + y = -3.292415527 Solving -2.8 + y = -3.292415527 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 = -3.292415527 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + y = -3.292415527 + 2.8 y = -3.292415527 + 2.8 Combine like terms: -3.292415527 + 2.8 = -0.492415527 y = -0.492415527 Simplifying y = -0.492415527Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.092415527, -0.492415527}
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