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Simplifying 5y2 + -29y + 41 = 0 Reorder the terms: 41 + -29y + 5y2 = 0 Solving 41 + -29y + 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'. 8.2 + -5.8y + y2 = 0 Move the constant term to the right: Add '-8.2' to each side of the equation. 8.2 + -5.8y + -8.2 + y2 = 0 + -8.2 Reorder the terms: 8.2 + -8.2 + -5.8y + y2 = 0 + -8.2 Combine like terms: 8.2 + -8.2 = 0.0 0.0 + -5.8y + y2 = 0 + -8.2 -5.8y + y2 = 0 + -8.2 Combine like terms: 0 + -8.2 = -8.2 -5.8y + y2 = -8.2 The y term is -5.8y. Take half its coefficient (-2.9). Square it (8.41) and add it to both sides. Add '8.41' to each side of the equation. -5.8y + 8.41 + y2 = -8.2 + 8.41 Reorder the terms: 8.41 + -5.8y + y2 = -8.2 + 8.41 Combine like terms: -8.2 + 8.41 = 0.21 8.41 + -5.8y + y2 = 0.21 Factor a perfect square on the left side: (y + -2.9)(y + -2.9) = 0.21 Calculate the square root of the right side: 0.458257569 Break this problem into two subproblems by setting (y + -2.9) equal to 0.458257569 and -0.458257569.Subproblem 1
y + -2.9 = 0.458257569 Simplifying y + -2.9 = 0.458257569 Reorder the terms: -2.9 + y = 0.458257569 Solving -2.9 + y = 0.458257569 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.9' to each side of the equation. -2.9 + 2.9 + y = 0.458257569 + 2.9 Combine like terms: -2.9 + 2.9 = 0.0 0.0 + y = 0.458257569 + 2.9 y = 0.458257569 + 2.9 Combine like terms: 0.458257569 + 2.9 = 3.358257569 y = 3.358257569 Simplifying y = 3.358257569Subproblem 2
y + -2.9 = -0.458257569 Simplifying y + -2.9 = -0.458257569 Reorder the terms: -2.9 + y = -0.458257569 Solving -2.9 + y = -0.458257569 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.9' to each side of the equation. -2.9 + 2.9 + y = -0.458257569 + 2.9 Combine like terms: -2.9 + 2.9 = 0.0 0.0 + y = -0.458257569 + 2.9 y = -0.458257569 + 2.9 Combine like terms: -0.458257569 + 2.9 = 2.441742431 y = 2.441742431 Simplifying y = 2.441742431Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.358257569, 2.441742431}
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