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Simplifying 4y + 5 + -4.2 + -5y2 + 2 = 0 Reorder the terms: 5 + -4.2 + 2 + 4y + -5y2 = 0 Combine like terms: 5 + -4.2 = 0.8 0.8 + 2 + 4y + -5y2 = 0 Combine like terms: 0.8 + 2 = 2.8 2.8 + 4y + -5y2 = 0 Solving 2.8 + 4y + -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'. -0.56 + -0.8y + y2 = 0 Move the constant term to the right: Add '0.56' to each side of the equation. -0.56 + -0.8y + 0.56 + y2 = 0 + 0.56 Reorder the terms: -0.56 + 0.56 + -0.8y + y2 = 0 + 0.56 Combine like terms: -0.56 + 0.56 = 0.00 0.00 + -0.8y + y2 = 0 + 0.56 -0.8y + y2 = 0 + 0.56 Combine like terms: 0 + 0.56 = 0.56 -0.8y + y2 = 0.56 The y term is -0.8y. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8y + 0.16 + y2 = 0.56 + 0.16 Reorder the terms: 0.16 + -0.8y + y2 = 0.56 + 0.16 Combine like terms: 0.56 + 0.16 = 0.72 0.16 + -0.8y + y2 = 0.72 Factor a perfect square on the left side: (y + -0.4)(y + -0.4) = 0.72 Calculate the square root of the right side: 0.848528137 Break this problem into two subproblems by setting (y + -0.4) equal to 0.848528137 and -0.848528137.Subproblem 1
y + -0.4 = 0.848528137 Simplifying y + -0.4 = 0.848528137 Reorder the terms: -0.4 + y = 0.848528137 Solving -0.4 + y = 0.848528137 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + y = 0.848528137 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + y = 0.848528137 + 0.4 y = 0.848528137 + 0.4 Combine like terms: 0.848528137 + 0.4 = 1.248528137 y = 1.248528137 Simplifying y = 1.248528137Subproblem 2
y + -0.4 = -0.848528137 Simplifying y + -0.4 = -0.848528137 Reorder the terms: -0.4 + y = -0.848528137 Solving -0.4 + y = -0.848528137 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + y = -0.848528137 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + y = -0.848528137 + 0.4 y = -0.848528137 + 0.4 Combine like terms: -0.848528137 + 0.4 = -0.448528137 y = -0.448528137 Simplifying y = -0.448528137Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.248528137, -0.448528137}
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