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Simplifying 5(y2 + -8y + -1) = 0 Reorder the terms: 5(-1 + -8y + y2) = 0 (-1 * 5 + -8y * 5 + y2 * 5) = 0 (-5 + -40y + 5y2) = 0 Solving -5 + -40y + 5y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '5'. 5(-1 + -8y + y2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-1 + -8y + y2)' equal to zero and attempt to solve: Simplifying -1 + -8y + y2 = 0 Solving -1 + -8y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -8y + 1 + y2 = 0 + 1 Reorder the terms: -1 + 1 + -8y + y2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -8y + y2 = 0 + 1 -8y + y2 = 0 + 1 Combine like terms: 0 + 1 = 1 -8y + y2 = 1 The y term is -8y. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8y + 16 + y2 = 1 + 16 Reorder the terms: 16 + -8y + y2 = 1 + 16 Combine like terms: 1 + 16 = 17 16 + -8y + y2 = 17 Factor a perfect square on the left side: (y + -4)(y + -4) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (y + -4) equal to 4.123105626 and -4.123105626.Subproblem 1
y + -4 = 4.123105626 Simplifying y + -4 = 4.123105626 Reorder the terms: -4 + y = 4.123105626 Solving -4 + y = 4.123105626 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + y = 4.123105626 + 4 Combine like terms: -4 + 4 = 0 0 + y = 4.123105626 + 4 y = 4.123105626 + 4 Combine like terms: 4.123105626 + 4 = 8.123105626 y = 8.123105626 Simplifying y = 8.123105626Subproblem 2
y + -4 = -4.123105626 Simplifying y + -4 = -4.123105626 Reorder the terms: -4 + y = -4.123105626 Solving -4 + y = -4.123105626 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + y = -4.123105626 + 4 Combine like terms: -4 + 4 = 0 0 + y = -4.123105626 + 4 y = -4.123105626 + 4 Combine like terms: -4.123105626 + 4 = -0.123105626 y = -0.123105626 Simplifying y = -0.123105626Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.123105626, -0.123105626}Solution
y = {8.123105626, -0.123105626}
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