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Simplifying 4y2 + 5y + -3 = 0 Reorder the terms: -3 + 5y + 4y2 = 0 Solving -3 + 5y + 4y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.75 + 1.25y + y2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 1.25y + 0.75 + y2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 1.25y + y2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 1.25y + y2 = 0 + 0.75 1.25y + y2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 1.25y + y2 = 0.75 The y term is 1.25y. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25y + 0.390625 + y2 = 0.75 + 0.390625 Reorder the terms: 0.390625 + 1.25y + y2 = 0.75 + 0.390625 Combine like terms: 0.75 + 0.390625 = 1.140625 0.390625 + 1.25y + y2 = 1.140625 Factor a perfect square on the left side: (y + 0.625)(y + 0.625) = 1.140625 Calculate the square root of the right side: 1.068000468 Break this problem into two subproblems by setting (y + 0.625) equal to 1.068000468 and -1.068000468.Subproblem 1
y + 0.625 = 1.068000468 Simplifying y + 0.625 = 1.068000468 Reorder the terms: 0.625 + y = 1.068000468 Solving 0.625 + y = 1.068000468 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + y = 1.068000468 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + y = 1.068000468 + -0.625 y = 1.068000468 + -0.625 Combine like terms: 1.068000468 + -0.625 = 0.443000468 y = 0.443000468 Simplifying y = 0.443000468Subproblem 2
y + 0.625 = -1.068000468 Simplifying y + 0.625 = -1.068000468 Reorder the terms: 0.625 + y = -1.068000468 Solving 0.625 + y = -1.068000468 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + y = -1.068000468 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + y = -1.068000468 + -0.625 y = -1.068000468 + -0.625 Combine like terms: -1.068000468 + -0.625 = -1.693000468 y = -1.693000468 Simplifying y = -1.693000468Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.443000468, -1.693000468}
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