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Simplifying 2y2 + 25y + -48 = 0 Reorder the terms: -48 + 25y + 2y2 = 0 Solving -48 + 25y + 2y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -24 + 12.5y + y2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + 12.5y + 24 + y2 = 0 + 24 Reorder the terms: -24 + 24 + 12.5y + y2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 12.5y + y2 = 0 + 24 12.5y + y2 = 0 + 24 Combine like terms: 0 + 24 = 24 12.5y + y2 = 24 The y term is 12.5y. Take half its coefficient (6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. 12.5y + 39.0625 + y2 = 24 + 39.0625 Reorder the terms: 39.0625 + 12.5y + y2 = 24 + 39.0625 Combine like terms: 24 + 39.0625 = 63.0625 39.0625 + 12.5y + y2 = 63.0625 Factor a perfect square on the left side: (y + 6.25)(y + 6.25) = 63.0625 Calculate the square root of the right side: 7.941190087 Break this problem into two subproblems by setting (y + 6.25) equal to 7.941190087 and -7.941190087.Subproblem 1
y + 6.25 = 7.941190087 Simplifying y + 6.25 = 7.941190087 Reorder the terms: 6.25 + y = 7.941190087 Solving 6.25 + y = 7.941190087 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + y = 7.941190087 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + y = 7.941190087 + -6.25 y = 7.941190087 + -6.25 Combine like terms: 7.941190087 + -6.25 = 1.691190087 y = 1.691190087 Simplifying y = 1.691190087Subproblem 2
y + 6.25 = -7.941190087 Simplifying y + 6.25 = -7.941190087 Reorder the terms: 6.25 + y = -7.941190087 Solving 6.25 + y = -7.941190087 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + y = -7.941190087 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + y = -7.941190087 + -6.25 y = -7.941190087 + -6.25 Combine like terms: -7.941190087 + -6.25 = -14.191190087 y = -14.191190087 Simplifying y = -14.191190087Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.691190087, -14.191190087}
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