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Simplifying 4y2 + 5y + -25 = 0 Reorder the terms: -25 + 5y + 4y2 = 0 Solving -25 + 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'. -6.25 + 1.25y + y2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + 1.25y + 6.25 + y2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + 1.25y + y2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + 1.25y + y2 = 0 + 6.25 1.25y + y2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 1.25y + y2 = 6.25 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 = 6.25 + 0.390625 Reorder the terms: 0.390625 + 1.25y + y2 = 6.25 + 0.390625 Combine like terms: 6.25 + 0.390625 = 6.640625 0.390625 + 1.25y + y2 = 6.640625 Factor a perfect square on the left side: (y + 0.625)(y + 0.625) = 6.640625 Calculate the square root of the right side: 2.576941016 Break this problem into two subproblems by setting (y + 0.625) equal to 2.576941016 and -2.576941016.Subproblem 1
y + 0.625 = 2.576941016 Simplifying y + 0.625 = 2.576941016 Reorder the terms: 0.625 + y = 2.576941016 Solving 0.625 + y = 2.576941016 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 = 2.576941016 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + y = 2.576941016 + -0.625 y = 2.576941016 + -0.625 Combine like terms: 2.576941016 + -0.625 = 1.951941016 y = 1.951941016 Simplifying y = 1.951941016Subproblem 2
y + 0.625 = -2.576941016 Simplifying y + 0.625 = -2.576941016 Reorder the terms: 0.625 + y = -2.576941016 Solving 0.625 + y = -2.576941016 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 = -2.576941016 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + y = -2.576941016 + -0.625 y = -2.576941016 + -0.625 Combine like terms: -2.576941016 + -0.625 = -3.201941016 y = -3.201941016 Simplifying y = -3.201941016Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.951941016, -3.201941016}
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