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Simplifying 2y2 + 51y + -84 = 0 Reorder the terms: -84 + 51y + 2y2 = 0 Solving -84 + 51y + 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'. -42 + 25.5y + y2 = 0 Move the constant term to the right: Add '42' to each side of the equation. -42 + 25.5y + 42 + y2 = 0 + 42 Reorder the terms: -42 + 42 + 25.5y + y2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + 25.5y + y2 = 0 + 42 25.5y + y2 = 0 + 42 Combine like terms: 0 + 42 = 42 25.5y + y2 = 42 The y term is 25.5y. Take half its coefficient (12.75). Square it (162.5625) and add it to both sides. Add '162.5625' to each side of the equation. 25.5y + 162.5625 + y2 = 42 + 162.5625 Reorder the terms: 162.5625 + 25.5y + y2 = 42 + 162.5625 Combine like terms: 42 + 162.5625 = 204.5625 162.5625 + 25.5y + y2 = 204.5625 Factor a perfect square on the left side: (y + 12.75)(y + 12.75) = 204.5625 Calculate the square root of the right side: 14.30253474 Break this problem into two subproblems by setting (y + 12.75) equal to 14.30253474 and -14.30253474.Subproblem 1
y + 12.75 = 14.30253474 Simplifying y + 12.75 = 14.30253474 Reorder the terms: 12.75 + y = 14.30253474 Solving 12.75 + y = 14.30253474 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-12.75' to each side of the equation. 12.75 + -12.75 + y = 14.30253474 + -12.75 Combine like terms: 12.75 + -12.75 = 0.00 0.00 + y = 14.30253474 + -12.75 y = 14.30253474 + -12.75 Combine like terms: 14.30253474 + -12.75 = 1.55253474 y = 1.55253474 Simplifying y = 1.55253474Subproblem 2
y + 12.75 = -14.30253474 Simplifying y + 12.75 = -14.30253474 Reorder the terms: 12.75 + y = -14.30253474 Solving 12.75 + y = -14.30253474 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-12.75' to each side of the equation. 12.75 + -12.75 + y = -14.30253474 + -12.75 Combine like terms: 12.75 + -12.75 = 0.00 0.00 + y = -14.30253474 + -12.75 y = -14.30253474 + -12.75 Combine like terms: -14.30253474 + -12.75 = -27.05253474 y = -27.05253474 Simplifying y = -27.05253474Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.55253474, -27.05253474}
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