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Simplifying 7.84y2 + -7.84y + 1 = 0 Reorder the terms: 1 + -7.84y + 7.84y2 = 0 Solving 1 + -7.84y + 7.84y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 7.84 the coefficient of the squared term: Divide each side by '7.84'. 0.1275510204 + -1y + y2 = 0 Move the constant term to the right: Add '-0.1275510204' to each side of the equation. 0.1275510204 + -1y + -0.1275510204 + y2 = 0 + -0.1275510204 Reorder the terms: 0.1275510204 + -0.1275510204 + -1y + y2 = 0 + -0.1275510204 Combine like terms: 0.1275510204 + -0.1275510204 = 0.0000000000 0.0000000000 + -1y + y2 = 0 + -0.1275510204 -1y + y2 = 0 + -0.1275510204 Combine like terms: 0 + -0.1275510204 = -0.1275510204 -1y + y2 = -0.1275510204 The y term is -1y. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1y + 0.25 + y2 = -0.1275510204 + 0.25 Reorder the terms: 0.25 + -1y + y2 = -0.1275510204 + 0.25 Combine like terms: -0.1275510204 + 0.25 = 0.1224489796 0.25 + -1y + y2 = 0.1224489796 Factor a perfect square on the left side: (y + -0.5)(y + -0.5) = 0.1224489796 Calculate the square root of the right side: 0.349927106 Break this problem into two subproblems by setting (y + -0.5) equal to 0.349927106 and -0.349927106.Subproblem 1
y + -0.5 = 0.349927106 Simplifying y + -0.5 = 0.349927106 Reorder the terms: -0.5 + y = 0.349927106 Solving -0.5 + y = 0.349927106 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = 0.349927106 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = 0.349927106 + 0.5 y = 0.349927106 + 0.5 Combine like terms: 0.349927106 + 0.5 = 0.849927106 y = 0.849927106 Simplifying y = 0.849927106Subproblem 2
y + -0.5 = -0.349927106 Simplifying y + -0.5 = -0.349927106 Reorder the terms: -0.5 + y = -0.349927106 Solving -0.5 + y = -0.349927106 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = -0.349927106 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = -0.349927106 + 0.5 y = -0.349927106 + 0.5 Combine like terms: -0.349927106 + 0.5 = 0.150072894 y = 0.150072894 Simplifying y = 0.150072894Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.849927106, 0.150072894}
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