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Simplifying 5y2 + 3y = 17 Reorder the terms: 3y + 5y2 = 17 Solving 3y + 5y2 = 17 Solving for variable 'y'. Reorder the terms: -17 + 3y + 5y2 = 17 + -17 Combine like terms: 17 + -17 = 0 -17 + 3y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.4 + 0.6y + y2 = 0 Move the constant term to the right: Add '3.4' to each side of the equation. -3.4 + 0.6y + 3.4 + y2 = 0 + 3.4 Reorder the terms: -3.4 + 3.4 + 0.6y + y2 = 0 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + 0.6y + y2 = 0 + 3.4 0.6y + y2 = 0 + 3.4 Combine like terms: 0 + 3.4 = 3.4 0.6y + y2 = 3.4 The y term is 0.6y. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6y + 0.09 + y2 = 3.4 + 0.09 Reorder the terms: 0.09 + 0.6y + y2 = 3.4 + 0.09 Combine like terms: 3.4 + 0.09 = 3.49 0.09 + 0.6y + y2 = 3.49 Factor a perfect square on the left side: (y + 0.3)(y + 0.3) = 3.49 Calculate the square root of the right side: 1.868154169 Break this problem into two subproblems by setting (y + 0.3) equal to 1.868154169 and -1.868154169.Subproblem 1
y + 0.3 = 1.868154169 Simplifying y + 0.3 = 1.868154169 Reorder the terms: 0.3 + y = 1.868154169 Solving 0.3 + y = 1.868154169 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + y = 1.868154169 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + y = 1.868154169 + -0.3 y = 1.868154169 + -0.3 Combine like terms: 1.868154169 + -0.3 = 1.568154169 y = 1.568154169 Simplifying y = 1.568154169Subproblem 2
y + 0.3 = -1.868154169 Simplifying y + 0.3 = -1.868154169 Reorder the terms: 0.3 + y = -1.868154169 Solving 0.3 + y = -1.868154169 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + y = -1.868154169 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + y = -1.868154169 + -0.3 y = -1.868154169 + -0.3 Combine like terms: -1.868154169 + -0.3 = -2.168154169 y = -2.168154169 Simplifying y = -2.168154169Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.568154169, -2.168154169}
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