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Simplifying y2 + 91y + 98 = 0 Reorder the terms: 98 + 91y + y2 = 0 Solving 98 + 91y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-98' to each side of the equation. 98 + 91y + -98 + y2 = 0 + -98 Reorder the terms: 98 + -98 + 91y + y2 = 0 + -98 Combine like terms: 98 + -98 = 0 0 + 91y + y2 = 0 + -98 91y + y2 = 0 + -98 Combine like terms: 0 + -98 = -98 91y + y2 = -98 The y term is 91y. Take half its coefficient (45.5). Square it (2070.25) and add it to both sides. Add '2070.25' to each side of the equation. 91y + 2070.25 + y2 = -98 + 2070.25 Reorder the terms: 2070.25 + 91y + y2 = -98 + 2070.25 Combine like terms: -98 + 2070.25 = 1972.25 2070.25 + 91y + y2 = 1972.25 Factor a perfect square on the left side: (y + 45.5)(y + 45.5) = 1972.25 Calculate the square root of the right side: 44.410021392 Break this problem into two subproblems by setting (y + 45.5) equal to 44.410021392 and -44.410021392.Subproblem 1
y + 45.5 = 44.410021392 Simplifying y + 45.5 = 44.410021392 Reorder the terms: 45.5 + y = 44.410021392 Solving 45.5 + y = 44.410021392 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-45.5' to each side of the equation. 45.5 + -45.5 + y = 44.410021392 + -45.5 Combine like terms: 45.5 + -45.5 = 0.0 0.0 + y = 44.410021392 + -45.5 y = 44.410021392 + -45.5 Combine like terms: 44.410021392 + -45.5 = -1.089978608 y = -1.089978608 Simplifying y = -1.089978608Subproblem 2
y + 45.5 = -44.410021392 Simplifying y + 45.5 = -44.410021392 Reorder the terms: 45.5 + y = -44.410021392 Solving 45.5 + y = -44.410021392 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-45.5' to each side of the equation. 45.5 + -45.5 + y = -44.410021392 + -45.5 Combine like terms: 45.5 + -45.5 = 0.0 0.0 + y = -44.410021392 + -45.5 y = -44.410021392 + -45.5 Combine like terms: -44.410021392 + -45.5 = -89.910021392 y = -89.910021392 Simplifying y = -89.910021392Solution
The solution to the problem is based on the solutions from the subproblems. y = {-1.089978608, -89.910021392}
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