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Simplifying 4y2 + -1y + -48 = 0 Reorder the terms: -48 + -1y + 4y2 = 0 Solving -48 + -1y + 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'. -12 + -0.25y + y2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -0.25y + 12 + y2 = 0 + 12 Reorder the terms: -12 + 12 + -0.25y + y2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -0.25y + y2 = 0 + 12 -0.25y + y2 = 0 + 12 Combine like terms: 0 + 12 = 12 -0.25y + y2 = 12 The y term is -0.25y. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25y + 0.015625 + y2 = 12 + 0.015625 Reorder the terms: 0.015625 + -0.25y + y2 = 12 + 0.015625 Combine like terms: 12 + 0.015625 = 12.015625 0.015625 + -0.25y + y2 = 12.015625 Factor a perfect square on the left side: (y + -0.125)(y + -0.125) = 12.015625 Calculate the square root of the right side: 3.466356156 Break this problem into two subproblems by setting (y + -0.125) equal to 3.466356156 and -3.466356156.Subproblem 1
y + -0.125 = 3.466356156 Simplifying y + -0.125 = 3.466356156 Reorder the terms: -0.125 + y = 3.466356156 Solving -0.125 + y = 3.466356156 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + y = 3.466356156 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + y = 3.466356156 + 0.125 y = 3.466356156 + 0.125 Combine like terms: 3.466356156 + 0.125 = 3.591356156 y = 3.591356156 Simplifying y = 3.591356156Subproblem 2
y + -0.125 = -3.466356156 Simplifying y + -0.125 = -3.466356156 Reorder the terms: -0.125 + y = -3.466356156 Solving -0.125 + y = -3.466356156 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + y = -3.466356156 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + y = -3.466356156 + 0.125 y = -3.466356156 + 0.125 Combine like terms: -3.466356156 + 0.125 = -3.341356156 y = -3.341356156 Simplifying y = -3.341356156Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.591356156, -3.341356156}
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