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Simplifying 4y2 + -8y + -56 = 0 Reorder the terms: -56 + -8y + 4y2 = 0 Solving -56 + -8y + 4y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '4'. 4(-14 + -2y + y2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-14 + -2y + y2)' equal to zero and attempt to solve: Simplifying -14 + -2y + y2 = 0 Solving -14 + -2y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + -2y + 14 + y2 = 0 + 14 Reorder the terms: -14 + 14 + -2y + y2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -2y + y2 = 0 + 14 -2y + y2 = 0 + 14 Combine like terms: 0 + 14 = 14 -2y + y2 = 14 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 = 14 + 1 Reorder the terms: 1 + -2y + y2 = 14 + 1 Combine like terms: 14 + 1 = 15 1 + -2y + y2 = 15 Factor a perfect square on the left side: (y + -1)(y + -1) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (y + -1) equal to 3.872983346 and -3.872983346.Subproblem 1
y + -1 = 3.872983346 Simplifying y + -1 = 3.872983346 Reorder the terms: -1 + y = 3.872983346 Solving -1 + y = 3.872983346 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 = 3.872983346 + 1 Combine like terms: -1 + 1 = 0 0 + y = 3.872983346 + 1 y = 3.872983346 + 1 Combine like terms: 3.872983346 + 1 = 4.872983346 y = 4.872983346 Simplifying y = 4.872983346Subproblem 2
y + -1 = -3.872983346 Simplifying y + -1 = -3.872983346 Reorder the terms: -1 + y = -3.872983346 Solving -1 + y = -3.872983346 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 = -3.872983346 + 1 Combine like terms: -1 + 1 = 0 0 + y = -3.872983346 + 1 y = -3.872983346 + 1 Combine like terms: -3.872983346 + 1 = -2.872983346 y = -2.872983346 Simplifying y = -2.872983346Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.872983346, -2.872983346}Solution
y = {4.872983346, -2.872983346}
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