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Simplifying 2y2 + 9y + -2 = 0 Reorder the terms: -2 + 9y + 2y2 = 0 Solving -2 + 9y + 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'. -1 + 4.5y + y2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 4.5y + 1 + y2 = 0 + 1 Reorder the terms: -1 + 1 + 4.5y + y2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 4.5y + y2 = 0 + 1 4.5y + y2 = 0 + 1 Combine like terms: 0 + 1 = 1 4.5y + y2 = 1 The y term is 4.5y. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5y + 5.0625 + y2 = 1 + 5.0625 Reorder the terms: 5.0625 + 4.5y + y2 = 1 + 5.0625 Combine like terms: 1 + 5.0625 = 6.0625 5.0625 + 4.5y + y2 = 6.0625 Factor a perfect square on the left side: (y + 2.25)(y + 2.25) = 6.0625 Calculate the square root of the right side: 2.46221445 Break this problem into two subproblems by setting (y + 2.25) equal to 2.46221445 and -2.46221445.Subproblem 1
y + 2.25 = 2.46221445 Simplifying y + 2.25 = 2.46221445 Reorder the terms: 2.25 + y = 2.46221445 Solving 2.25 + y = 2.46221445 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + y = 2.46221445 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + y = 2.46221445 + -2.25 y = 2.46221445 + -2.25 Combine like terms: 2.46221445 + -2.25 = 0.21221445 y = 0.21221445 Simplifying y = 0.21221445Subproblem 2
y + 2.25 = -2.46221445 Simplifying y + 2.25 = -2.46221445 Reorder the terms: 2.25 + y = -2.46221445 Solving 2.25 + y = -2.46221445 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + y = -2.46221445 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + y = -2.46221445 + -2.25 y = -2.46221445 + -2.25 Combine like terms: -2.46221445 + -2.25 = -4.71221445 y = -4.71221445 Simplifying y = -4.71221445Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.21221445, -4.71221445}
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