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Simplifying 5y2 + 16y = 3 Reorder the terms: 16y + 5y2 = 3 Solving 16y + 5y2 = 3 Solving for variable 'y'. Reorder the terms: -3 + 16y + 5y2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 16y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.6 + 3.2y + y2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + 3.2y + 0.6 + y2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + 3.2y + y2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + 3.2y + y2 = 0 + 0.6 3.2y + y2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 3.2y + y2 = 0.6 The y term is 3.2y. Take half its coefficient (1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. 3.2y + 2.56 + y2 = 0.6 + 2.56 Reorder the terms: 2.56 + 3.2y + y2 = 0.6 + 2.56 Combine like terms: 0.6 + 2.56 = 3.16 2.56 + 3.2y + y2 = 3.16 Factor a perfect square on the left side: (y + 1.6)(y + 1.6) = 3.16 Calculate the square root of the right side: 1.777638883 Break this problem into two subproblems by setting (y + 1.6) equal to 1.777638883 and -1.777638883.Subproblem 1
y + 1.6 = 1.777638883 Simplifying y + 1.6 = 1.777638883 Reorder the terms: 1.6 + y = 1.777638883 Solving 1.6 + y = 1.777638883 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + y = 1.777638883 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + y = 1.777638883 + -1.6 y = 1.777638883 + -1.6 Combine like terms: 1.777638883 + -1.6 = 0.177638883 y = 0.177638883 Simplifying y = 0.177638883Subproblem 2
y + 1.6 = -1.777638883 Simplifying y + 1.6 = -1.777638883 Reorder the terms: 1.6 + y = -1.777638883 Solving 1.6 + y = -1.777638883 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + y = -1.777638883 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + y = -1.777638883 + -1.6 y = -1.777638883 + -1.6 Combine like terms: -1.777638883 + -1.6 = -3.377638883 y = -3.377638883 Simplifying y = -3.377638883Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.177638883, -3.377638883}
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