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Simplifying 5y2 + -28y + 20 = 0 Reorder the terms: 20 + -28y + 5y2 = 0 Solving 20 + -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'. 4 + -5.6y + y2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -5.6y + -4 + y2 = 0 + -4 Reorder the terms: 4 + -4 + -5.6y + y2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5.6y + y2 = 0 + -4 -5.6y + y2 = 0 + -4 Combine like terms: 0 + -4 = -4 -5.6y + y2 = -4 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 = -4 + 7.84 Reorder the terms: 7.84 + -5.6y + y2 = -4 + 7.84 Combine like terms: -4 + 7.84 = 3.84 7.84 + -5.6y + y2 = 3.84 Factor a perfect square on the left side: (y + -2.8)(y + -2.8) = 3.84 Calculate the square root of the right side: 1.959591794 Break this problem into two subproblems by setting (y + -2.8) equal to 1.959591794 and -1.959591794.Subproblem 1
y + -2.8 = 1.959591794 Simplifying y + -2.8 = 1.959591794 Reorder the terms: -2.8 + y = 1.959591794 Solving -2.8 + y = 1.959591794 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 = 1.959591794 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + y = 1.959591794 + 2.8 y = 1.959591794 + 2.8 Combine like terms: 1.959591794 + 2.8 = 4.759591794 y = 4.759591794 Simplifying y = 4.759591794Subproblem 2
y + -2.8 = -1.959591794 Simplifying y + -2.8 = -1.959591794 Reorder the terms: -2.8 + y = -1.959591794 Solving -2.8 + y = -1.959591794 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 = -1.959591794 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + y = -1.959591794 + 2.8 y = -1.959591794 + 2.8 Combine like terms: -1.959591794 + 2.8 = 0.840408206 y = 0.840408206 Simplifying y = 0.840408206Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.759591794, 0.840408206}
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