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Simplifying y2 + -8y + 6 = 0 Reorder the terms: 6 + -8y + y2 = 0 Solving 6 + -8y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -8y + -6 + y2 = 0 + -6 Reorder the terms: 6 + -6 + -8y + y2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -8y + y2 = 0 + -6 -8y + y2 = 0 + -6 Combine like terms: 0 + -6 = -6 -8y + y2 = -6 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 = -6 + 16 Reorder the terms: 16 + -8y + y2 = -6 + 16 Combine like terms: -6 + 16 = 10 16 + -8y + y2 = 10 Factor a perfect square on the left side: (y + -4)(y + -4) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (y + -4) equal to 3.16227766 and -3.16227766.Subproblem 1
y + -4 = 3.16227766 Simplifying y + -4 = 3.16227766 Reorder the terms: -4 + y = 3.16227766 Solving -4 + y = 3.16227766 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 = 3.16227766 + 4 Combine like terms: -4 + 4 = 0 0 + y = 3.16227766 + 4 y = 3.16227766 + 4 Combine like terms: 3.16227766 + 4 = 7.16227766 y = 7.16227766 Simplifying y = 7.16227766Subproblem 2
y + -4 = -3.16227766 Simplifying y + -4 = -3.16227766 Reorder the terms: -4 + y = -3.16227766 Solving -4 + y = -3.16227766 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 = -3.16227766 + 4 Combine like terms: -4 + 4 = 0 0 + y = -3.16227766 + 4 y = -3.16227766 + 4 Combine like terms: -3.16227766 + 4 = 0.83772234 y = 0.83772234 Simplifying y = 0.83772234Solution
The solution to the problem is based on the solutions from the subproblems. y = {7.16227766, 0.83772234}
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