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Simplifying 2 + -3.5y + -9.75y2 = 0 Solving 2 + -3.5y + -9.75y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -9.75 the coefficient of the squared term: Divide each side by '-9.75'. -0.2051282051 + 0.358974359y + y2 = 0 Move the constant term to the right: Add '0.2051282051' to each side of the equation. -0.2051282051 + 0.358974359y + 0.2051282051 + y2 = 0 + 0.2051282051 Reorder the terms: -0.2051282051 + 0.2051282051 + 0.358974359y + y2 = 0 + 0.2051282051 Combine like terms: -0.2051282051 + 0.2051282051 = 0.0000000000 0.0000000000 + 0.358974359y + y2 = 0 + 0.2051282051 0.358974359y + y2 = 0 + 0.2051282051 Combine like terms: 0 + 0.2051282051 = 0.2051282051 0.358974359y + y2 = 0.2051282051 The y term is 0.358974359y. Take half its coefficient (0.1794871795). Square it (0.03221564760) and add it to both sides. Add '0.03221564760' to each side of the equation. 0.358974359y + 0.03221564760 + y2 = 0.2051282051 + 0.03221564760 Reorder the terms: 0.03221564760 + 0.358974359y + y2 = 0.2051282051 + 0.03221564760 Combine like terms: 0.2051282051 + 0.03221564760 = 0.2373438527 0.03221564760 + 0.358974359y + y2 = 0.2373438527 Factor a perfect square on the left side: (y + 0.1794871795)(y + 0.1794871795) = 0.2373438527 Calculate the square root of the right side: 0.487179487 Break this problem into two subproblems by setting (y + 0.1794871795) equal to 0.487179487 and -0.487179487.Subproblem 1
y + 0.1794871795 = 0.487179487 Simplifying y + 0.1794871795 = 0.487179487 Reorder the terms: 0.1794871795 + y = 0.487179487 Solving 0.1794871795 + y = 0.487179487 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.1794871795' to each side of the equation. 0.1794871795 + -0.1794871795 + y = 0.487179487 + -0.1794871795 Combine like terms: 0.1794871795 + -0.1794871795 = 0.0000000000 0.0000000000 + y = 0.487179487 + -0.1794871795 y = 0.487179487 + -0.1794871795 Combine like terms: 0.487179487 + -0.1794871795 = 0.3076923075 y = 0.3076923075 Simplifying y = 0.3076923075Subproblem 2
y + 0.1794871795 = -0.487179487 Simplifying y + 0.1794871795 = -0.487179487 Reorder the terms: 0.1794871795 + y = -0.487179487 Solving 0.1794871795 + y = -0.487179487 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.1794871795' to each side of the equation. 0.1794871795 + -0.1794871795 + y = -0.487179487 + -0.1794871795 Combine like terms: 0.1794871795 + -0.1794871795 = 0.0000000000 0.0000000000 + y = -0.487179487 + -0.1794871795 y = -0.487179487 + -0.1794871795 Combine like terms: -0.487179487 + -0.1794871795 = -0.6666666665 y = -0.6666666665 Simplifying y = -0.6666666665Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.3076923075, -0.6666666665}
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