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Simplifying 5y2 + -10y + -56 = 0 Reorder the terms: -56 + -10y + 5y2 = 0 Solving -56 + -10y + 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'. -11.2 + -2y + y2 = 0 Move the constant term to the right: Add '11.2' to each side of the equation. -11.2 + -2y + 11.2 + y2 = 0 + 11.2 Reorder the terms: -11.2 + 11.2 + -2y + y2 = 0 + 11.2 Combine like terms: -11.2 + 11.2 = 0.0 0.0 + -2y + y2 = 0 + 11.2 -2y + y2 = 0 + 11.2 Combine like terms: 0 + 11.2 = 11.2 -2y + y2 = 11.2 The y term is -2y. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2y + 1 + y2 = 11.2 + 1 Reorder the terms: 1 + -2y + y2 = 11.2 + 1 Combine like terms: 11.2 + 1 = 12.2 1 + -2y + y2 = 12.2 Factor a perfect square on the left side: (y + -1)(y + -1) = 12.2 Calculate the square root of the right side: 3.492849839 Break this problem into two subproblems by setting (y + -1) equal to 3.492849839 and -3.492849839.Subproblem 1
y + -1 = 3.492849839 Simplifying y + -1 = 3.492849839 Reorder the terms: -1 + y = 3.492849839 Solving -1 + y = 3.492849839 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = 3.492849839 + 1 Combine like terms: -1 + 1 = 0 0 + y = 3.492849839 + 1 y = 3.492849839 + 1 Combine like terms: 3.492849839 + 1 = 4.492849839 y = 4.492849839 Simplifying y = 4.492849839Subproblem 2
y + -1 = -3.492849839 Simplifying y + -1 = -3.492849839 Reorder the terms: -1 + y = -3.492849839 Solving -1 + y = -3.492849839 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = -3.492849839 + 1 Combine like terms: -1 + 1 = 0 0 + y = -3.492849839 + 1 y = -3.492849839 + 1 Combine like terms: -3.492849839 + 1 = -2.492849839 y = -2.492849839 Simplifying y = -2.492849839Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.492849839, -2.492849839}
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