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Simplifying 0 = y2 + 28y + 98 Reorder the terms: 0 = 98 + 28y + y2 Solving 0 = 98 + 28y + y2 Solving for variable 'y'. Combine like terms: 0 + -98 = -98 -98 + -28y + -1y2 = 98 + 28y + y2 + -98 + -28y + -1y2 Reorder the terms: -98 + -28y + -1y2 = 98 + -98 + 28y + -28y + y2 + -1y2 Combine like terms: 98 + -98 = 0 -98 + -28y + -1y2 = 0 + 28y + -28y + y2 + -1y2 -98 + -28y + -1y2 = 28y + -28y + y2 + -1y2 Combine like terms: 28y + -28y = 0 -98 + -28y + -1y2 = 0 + y2 + -1y2 -98 + -28y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -98 + -28y + -1y2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(98 + 28y + y2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(98 + 28y + y2)' equal to zero and attempt to solve: Simplifying 98 + 28y + y2 = 0 Solving 98 + 28y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-98' to each side of the equation. 98 + 28y + -98 + y2 = 0 + -98 Reorder the terms: 98 + -98 + 28y + y2 = 0 + -98 Combine like terms: 98 + -98 = 0 0 + 28y + y2 = 0 + -98 28y + y2 = 0 + -98 Combine like terms: 0 + -98 = -98 28y + y2 = -98 The y term is 28y. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28y + 196 + y2 = -98 + 196 Reorder the terms: 196 + 28y + y2 = -98 + 196 Combine like terms: -98 + 196 = 98 196 + 28y + y2 = 98 Factor a perfect square on the left side: (y + 14)(y + 14) = 98 Calculate the square root of the right side: 9.899494937 Break this problem into two subproblems by setting (y + 14) equal to 9.899494937 and -9.899494937.Subproblem 1
y + 14 = 9.899494937 Simplifying y + 14 = 9.899494937 Reorder the terms: 14 + y = 9.899494937 Solving 14 + y = 9.899494937 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + y = 9.899494937 + -14 Combine like terms: 14 + -14 = 0 0 + y = 9.899494937 + -14 y = 9.899494937 + -14 Combine like terms: 9.899494937 + -14 = -4.100505063 y = -4.100505063 Simplifying y = -4.100505063Subproblem 2
y + 14 = -9.899494937 Simplifying y + 14 = -9.899494937 Reorder the terms: 14 + y = -9.899494937 Solving 14 + y = -9.899494937 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + y = -9.899494937 + -14 Combine like terms: 14 + -14 = 0 0 + y = -9.899494937 + -14 y = -9.899494937 + -14 Combine like terms: -9.899494937 + -14 = -23.899494937 y = -23.899494937 Simplifying y = -23.899494937Solution
The solution to the problem is based on the solutions from the subproblems. y = {-4.100505063, -23.899494937}Solution
y = {-4.100505063, -23.899494937}
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