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Simplifying 3.5y + 2y2 = 1 Solving 3.5y + 2y2 = 1 Solving for variable 'y'. Reorder the terms: -1 + 3.5y + 2y2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 3.5y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + 1.75y + y2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 1.75y + 0.5 + y2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 1.75y + y2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 1.75y + y2 = 0 + 0.5 1.75y + y2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 1.75y + y2 = 0.5 The y term is 1.75y. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75y + 0.765625 + y2 = 0.5 + 0.765625 Reorder the terms: 0.765625 + 1.75y + y2 = 0.5 + 0.765625 Combine like terms: 0.5 + 0.765625 = 1.265625 0.765625 + 1.75y + y2 = 1.265625 Factor a perfect square on the left side: (y + 0.875)(y + 0.875) = 1.265625 Calculate the square root of the right side: 1.125 Break this problem into two subproblems by setting (y + 0.875) equal to 1.125 and -1.125.Subproblem 1
y + 0.875 = 1.125 Simplifying y + 0.875 = 1.125 Reorder the terms: 0.875 + y = 1.125 Solving 0.875 + y = 1.125 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + y = 1.125 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + y = 1.125 + -0.875 y = 1.125 + -0.875 Combine like terms: 1.125 + -0.875 = 0.25 y = 0.25 Simplifying y = 0.25Subproblem 2
y + 0.875 = -1.125 Simplifying y + 0.875 = -1.125 Reorder the terms: 0.875 + y = -1.125 Solving 0.875 + y = -1.125 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + y = -1.125 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + y = -1.125 + -0.875 y = -1.125 + -0.875 Combine like terms: -1.125 + -0.875 = -2 y = -2 Simplifying y = -2Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.25, -2}
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