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Simplifying 53y2 + -4y + -48 = 0 Reorder the terms: -48 + -4y + 53y2 = 0 Solving -48 + -4y + 53y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 53 the coefficient of the squared term: Divide each side by '53'. -0.9056603774 + -0.07547169811y + y2 = 0 Move the constant term to the right: Add '0.9056603774' to each side of the equation. -0.9056603774 + -0.07547169811y + 0.9056603774 + y2 = 0 + 0.9056603774 Reorder the terms: -0.9056603774 + 0.9056603774 + -0.07547169811y + y2 = 0 + 0.9056603774 Combine like terms: -0.9056603774 + 0.9056603774 = 0.0000000000 0.0000000000 + -0.07547169811y + y2 = 0 + 0.9056603774 -0.07547169811y + y2 = 0 + 0.9056603774 Combine like terms: 0 + 0.9056603774 = 0.9056603774 -0.07547169811y + y2 = 0.9056603774 The y term is -0.07547169811y. Take half its coefficient (-0.03773584906). Square it (0.001423994304) and add it to both sides. Add '0.001423994304' to each side of the equation. -0.07547169811y + 0.001423994304 + y2 = 0.9056603774 + 0.001423994304 Reorder the terms: 0.001423994304 + -0.07547169811y + y2 = 0.9056603774 + 0.001423994304 Combine like terms: 0.9056603774 + 0.001423994304 = 0.907084371704 0.001423994304 + -0.07547169811y + y2 = 0.907084371704 Factor a perfect square on the left side: (y + -0.03773584906)(y + -0.03773584906) = 0.907084371704 Calculate the square root of the right side: 0.952409771 Break this problem into two subproblems by setting (y + -0.03773584906) equal to 0.952409771 and -0.952409771.Subproblem 1
y + -0.03773584906 = 0.952409771 Simplifying y + -0.03773584906 = 0.952409771 Reorder the terms: -0.03773584906 + y = 0.952409771 Solving -0.03773584906 + y = 0.952409771 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.03773584906' to each side of the equation. -0.03773584906 + 0.03773584906 + y = 0.952409771 + 0.03773584906 Combine like terms: -0.03773584906 + 0.03773584906 = 0.00000000000 0.00000000000 + y = 0.952409771 + 0.03773584906 y = 0.952409771 + 0.03773584906 Combine like terms: 0.952409771 + 0.03773584906 = 0.99014562006 y = 0.99014562006 Simplifying y = 0.99014562006Subproblem 2
y + -0.03773584906 = -0.952409771 Simplifying y + -0.03773584906 = -0.952409771 Reorder the terms: -0.03773584906 + y = -0.952409771 Solving -0.03773584906 + y = -0.952409771 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.03773584906' to each side of the equation. -0.03773584906 + 0.03773584906 + y = -0.952409771 + 0.03773584906 Combine like terms: -0.03773584906 + 0.03773584906 = 0.00000000000 0.00000000000 + y = -0.952409771 + 0.03773584906 y = -0.952409771 + 0.03773584906 Combine like terms: -0.952409771 + 0.03773584906 = -0.91467392194 y = -0.91467392194 Simplifying y = -0.91467392194Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.99014562006, -0.91467392194}
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