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Simplifying 5y2 + 5y + -9 = 0 Reorder the terms: -9 + 5y + 5y2 = 0 Solving -9 + 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'. -1.8 + y + y2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + y + 1.8 + y2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + y + y2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + y + y2 = 0 + 1.8 y + y2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 y + y2 = 1.8 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 = 1.8 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + y2 = 1.8 + 0.25 Combine like terms: 1.8 + 0.25 = 2.05 1.25 + y2 = 2.05 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = 2.05 Calculate the square root of the right side: 1.431782106 Break this problem into two subproblems by setting (y + 0.5) equal to 1.431782106 and -1.431782106.Subproblem 1
y + 0.5 = 1.431782106 Simplifying y + 0.5 = 1.431782106 Reorder the terms: 0.5 + y = 1.431782106 Solving 0.5 + y = 1.431782106 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 = 1.431782106 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 1.431782106 + -0.5 y = 1.431782106 + -0.5 Combine like terms: 1.431782106 + -0.5 = 0.931782106 y = 0.931782106 Simplifying y = 0.931782106Subproblem 2
y + 0.5 = -1.431782106 Simplifying y + 0.5 = -1.431782106 Reorder the terms: 0.5 + y = -1.431782106 Solving 0.5 + y = -1.431782106 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 = -1.431782106 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -1.431782106 + -0.5 y = -1.431782106 + -0.5 Combine like terms: -1.431782106 + -0.5 = -1.931782106 y = -1.931782106 Simplifying y = -1.931782106Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.931782106, -1.931782106}
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