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Simplifying 5y2 + 2y + -34 = 0 Reorder the terms: -34 + 2y + 5y2 = 0 Solving -34 + 2y + 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'. -6.8 + 0.4y + y2 = 0 Move the constant term to the right: Add '6.8' to each side of the equation. -6.8 + 0.4y + 6.8 + y2 = 0 + 6.8 Reorder the terms: -6.8 + 6.8 + 0.4y + y2 = 0 + 6.8 Combine like terms: -6.8 + 6.8 = 0.0 0.0 + 0.4y + y2 = 0 + 6.8 0.4y + y2 = 0 + 6.8 Combine like terms: 0 + 6.8 = 6.8 0.4y + y2 = 6.8 The y term is 0.4y. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4y + 0.04 + y2 = 6.8 + 0.04 Reorder the terms: 0.04 + 0.4y + y2 = 6.8 + 0.04 Combine like terms: 6.8 + 0.04 = 6.84 0.04 + 0.4y + y2 = 6.84 Factor a perfect square on the left side: (y + 0.2)(y + 0.2) = 6.84 Calculate the square root of the right side: 2.615339366 Break this problem into two subproblems by setting (y + 0.2) equal to 2.615339366 and -2.615339366.Subproblem 1
y + 0.2 = 2.615339366 Simplifying y + 0.2 = 2.615339366 Reorder the terms: 0.2 + y = 2.615339366 Solving 0.2 + y = 2.615339366 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + y = 2.615339366 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + y = 2.615339366 + -0.2 y = 2.615339366 + -0.2 Combine like terms: 2.615339366 + -0.2 = 2.415339366 y = 2.415339366 Simplifying y = 2.415339366Subproblem 2
y + 0.2 = -2.615339366 Simplifying y + 0.2 = -2.615339366 Reorder the terms: 0.2 + y = -2.615339366 Solving 0.2 + y = -2.615339366 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + y = -2.615339366 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + y = -2.615339366 + -0.2 y = -2.615339366 + -0.2 Combine like terms: -2.615339366 + -0.2 = -2.815339366 y = -2.815339366 Simplifying y = -2.815339366Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.415339366, -2.815339366}
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