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Simplifying 5y2 + 29y + 8 = 0 Reorder the terms: 8 + 29y + 5y2 = 0 Solving 8 + 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'. 1.6 + 5.8y + y2 = 0 Move the constant term to the right: Add '-1.6' to each side of the equation. 1.6 + 5.8y + -1.6 + y2 = 0 + -1.6 Reorder the terms: 1.6 + -1.6 + 5.8y + y2 = 0 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + 5.8y + y2 = 0 + -1.6 5.8y + y2 = 0 + -1.6 Combine like terms: 0 + -1.6 = -1.6 5.8y + y2 = -1.6 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 = -1.6 + 8.41 Reorder the terms: 8.41 + 5.8y + y2 = -1.6 + 8.41 Combine like terms: -1.6 + 8.41 = 6.81 8.41 + 5.8y + y2 = 6.81 Factor a perfect square on the left side: (y + 2.9)(y + 2.9) = 6.81 Calculate the square root of the right side: 2.60959767 Break this problem into two subproblems by setting (y + 2.9) equal to 2.60959767 and -2.60959767.Subproblem 1
y + 2.9 = 2.60959767 Simplifying y + 2.9 = 2.60959767 Reorder the terms: 2.9 + y = 2.60959767 Solving 2.9 + y = 2.60959767 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 = 2.60959767 + -2.9 Combine like terms: 2.9 + -2.9 = 0.0 0.0 + y = 2.60959767 + -2.9 y = 2.60959767 + -2.9 Combine like terms: 2.60959767 + -2.9 = -0.29040233 y = -0.29040233 Simplifying y = -0.29040233Subproblem 2
y + 2.9 = -2.60959767 Simplifying y + 2.9 = -2.60959767 Reorder the terms: 2.9 + y = -2.60959767 Solving 2.9 + y = -2.60959767 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 = -2.60959767 + -2.9 Combine like terms: 2.9 + -2.9 = 0.0 0.0 + y = -2.60959767 + -2.9 y = -2.60959767 + -2.9 Combine like terms: -2.60959767 + -2.9 = -5.50959767 y = -5.50959767 Simplifying y = -5.50959767Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.29040233, -5.50959767}
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