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Simplifying 2y2 + -7y + -18 = 0 Reorder the terms: -18 + -7y + 2y2 = 0 Solving -18 + -7y + 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'. -9 + -3.5y + y2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -3.5y + 9 + y2 = 0 + 9 Reorder the terms: -9 + 9 + -3.5y + y2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -3.5y + y2 = 0 + 9 -3.5y + y2 = 0 + 9 Combine like terms: 0 + 9 = 9 -3.5y + y2 = 9 The y term is -3.5y. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5y + 3.0625 + y2 = 9 + 3.0625 Reorder the terms: 3.0625 + -3.5y + y2 = 9 + 3.0625 Combine like terms: 9 + 3.0625 = 12.0625 3.0625 + -3.5y + y2 = 12.0625 Factor a perfect square on the left side: (y + -1.75)(y + -1.75) = 12.0625 Calculate the square root of the right side: 3.473110997 Break this problem into two subproblems by setting (y + -1.75) equal to 3.473110997 and -3.473110997.Subproblem 1
y + -1.75 = 3.473110997 Simplifying y + -1.75 = 3.473110997 Reorder the terms: -1.75 + y = 3.473110997 Solving -1.75 + y = 3.473110997 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + y = 3.473110997 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + y = 3.473110997 + 1.75 y = 3.473110997 + 1.75 Combine like terms: 3.473110997 + 1.75 = 5.223110997 y = 5.223110997 Simplifying y = 5.223110997Subproblem 2
y + -1.75 = -3.473110997 Simplifying y + -1.75 = -3.473110997 Reorder the terms: -1.75 + y = -3.473110997 Solving -1.75 + y = -3.473110997 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + y = -3.473110997 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + y = -3.473110997 + 1.75 y = -3.473110997 + 1.75 Combine like terms: -3.473110997 + 1.75 = -1.723110997 y = -1.723110997 Simplifying y = -1.723110997Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.223110997, -1.723110997}
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