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Simplifying 5y2 + 5y + -74 = 0 Reorder the terms: -74 + 5y + 5y2 = 0 Solving -74 + 5y + 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'. -14.8 + y + y2 = 0 Move the constant term to the right: Add '14.8' to each side of the equation. -14.8 + y + 14.8 + y2 = 0 + 14.8 Reorder the terms: -14.8 + 14.8 + y + y2 = 0 + 14.8 Combine like terms: -14.8 + 14.8 = 0.0 0.0 + y + y2 = 0 + 14.8 y + y2 = 0 + 14.8 Combine like terms: 0 + 14.8 = 14.8 y + y2 = 14.8 The y term is y. 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. + 0.25 + y2 = 14.8 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + y2 = 14.8 + 0.25 Combine like terms: 14.8 + 0.25 = 15.05 1.25 + y2 = 15.05 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = 15.05 Calculate the square root of the right side: 3.879432948 Break this problem into two subproblems by setting (y + 0.5) equal to 3.879432948 and -3.879432948.Subproblem 1
y + 0.5 = 3.879432948 Simplifying y + 0.5 = 3.879432948 Reorder the terms: 0.5 + y = 3.879432948 Solving 0.5 + y = 3.879432948 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 = 3.879432948 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 3.879432948 + -0.5 y = 3.879432948 + -0.5 Combine like terms: 3.879432948 + -0.5 = 3.379432948 y = 3.379432948 Simplifying y = 3.379432948Subproblem 2
y + 0.5 = -3.879432948 Simplifying y + 0.5 = -3.879432948 Reorder the terms: 0.5 + y = -3.879432948 Solving 0.5 + y = -3.879432948 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 = -3.879432948 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -3.879432948 + -0.5 y = -3.879432948 + -0.5 Combine like terms: -3.879432948 + -0.5 = -4.379432948 y = -4.379432948 Simplifying y = -4.379432948Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.379432948, -4.379432948}
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