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Simplifying 4y2 + 3y = 4 Reorder the terms: 3y + 4y2 = 4 Solving 3y + 4y2 = 4 Solving for variable 'y'. Reorder the terms: -4 + 3y + 4y2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 3y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1 + 0.75y + y2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.75y + 1 + y2 = 0 + 1 Reorder the terms: -1 + 1 + 0.75y + y2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.75y + y2 = 0 + 1 0.75y + y2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.75y + y2 = 1 The y term is 0.75y. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75y + 0.140625 + y2 = 1 + 0.140625 Reorder the terms: 0.140625 + 0.75y + y2 = 1 + 0.140625 Combine like terms: 1 + 0.140625 = 1.140625 0.140625 + 0.75y + y2 = 1.140625 Factor a perfect square on the left side: (y + 0.375)(y + 0.375) = 1.140625 Calculate the square root of the right side: 1.068000468 Break this problem into two subproblems by setting (y + 0.375) equal to 1.068000468 and -1.068000468.Subproblem 1
y + 0.375 = 1.068000468 Simplifying y + 0.375 = 1.068000468 Reorder the terms: 0.375 + y = 1.068000468 Solving 0.375 + y = 1.068000468 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + y = 1.068000468 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + y = 1.068000468 + -0.375 y = 1.068000468 + -0.375 Combine like terms: 1.068000468 + -0.375 = 0.693000468 y = 0.693000468 Simplifying y = 0.693000468Subproblem 2
y + 0.375 = -1.068000468 Simplifying y + 0.375 = -1.068000468 Reorder the terms: 0.375 + y = -1.068000468 Solving 0.375 + y = -1.068000468 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + y = -1.068000468 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + y = -1.068000468 + -0.375 y = -1.068000468 + -0.375 Combine like terms: -1.068000468 + -0.375 = -1.443000468 y = -1.443000468 Simplifying y = -1.443000468Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.693000468, -1.443000468}
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