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Simplifying y2 + -10y + -8 = 0 Reorder the terms: -8 + -10y + y2 = 0 Solving -8 + -10y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -10y + 8 + y2 = 0 + 8 Reorder the terms: -8 + 8 + -10y + y2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -10y + y2 = 0 + 8 -10y + y2 = 0 + 8 Combine like terms: 0 + 8 = 8 -10y + y2 = 8 The y term is -10y. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10y + 25 + y2 = 8 + 25 Reorder the terms: 25 + -10y + y2 = 8 + 25 Combine like terms: 8 + 25 = 33 25 + -10y + y2 = 33 Factor a perfect square on the left side: (y + -5)(y + -5) = 33 Calculate the square root of the right side: 5.744562647 Break this problem into two subproblems by setting (y + -5) equal to 5.744562647 and -5.744562647.Subproblem 1
y + -5 = 5.744562647 Simplifying y + -5 = 5.744562647 Reorder the terms: -5 + y = 5.744562647 Solving -5 + y = 5.744562647 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + y = 5.744562647 + 5 Combine like terms: -5 + 5 = 0 0 + y = 5.744562647 + 5 y = 5.744562647 + 5 Combine like terms: 5.744562647 + 5 = 10.744562647 y = 10.744562647 Simplifying y = 10.744562647Subproblem 2
y + -5 = -5.744562647 Simplifying y + -5 = -5.744562647 Reorder the terms: -5 + y = -5.744562647 Solving -5 + y = -5.744562647 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + y = -5.744562647 + 5 Combine like terms: -5 + 5 = 0 0 + y = -5.744562647 + 5 y = -5.744562647 + 5 Combine like terms: -5.744562647 + 5 = -0.744562647 y = -0.744562647 Simplifying y = -0.744562647Solution
The solution to the problem is based on the solutions from the subproblems. y = {10.744562647, -0.744562647}
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