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Simplifying 8y + 8 = y2 Reorder the terms: 8 + 8y = y2 Solving 8 + 8y = y2 Solving for variable 'y'. Combine like terms: y2 + -1y2 = 0 8 + 8y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -8 + -8y + y2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -8y + 8 + y2 = 0 + 8 Reorder the terms: -8 + 8 + -8y + y2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -8y + y2 = 0 + 8 -8y + y2 = 0 + 8 Combine like terms: 0 + 8 = 8 -8y + y2 = 8 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 = 8 + 16 Reorder the terms: 16 + -8y + y2 = 8 + 16 Combine like terms: 8 + 16 = 24 16 + -8y + y2 = 24 Factor a perfect square on the left side: (y + -4)(y + -4) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (y + -4) equal to 4.898979486 and -4.898979486.Subproblem 1
y + -4 = 4.898979486 Simplifying y + -4 = 4.898979486 Reorder the terms: -4 + y = 4.898979486 Solving -4 + y = 4.898979486 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 = 4.898979486 + 4 Combine like terms: -4 + 4 = 0 0 + y = 4.898979486 + 4 y = 4.898979486 + 4 Combine like terms: 4.898979486 + 4 = 8.898979486 y = 8.898979486 Simplifying y = 8.898979486Subproblem 2
y + -4 = -4.898979486 Simplifying y + -4 = -4.898979486 Reorder the terms: -4 + y = -4.898979486 Solving -4 + y = -4.898979486 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 = -4.898979486 + 4 Combine like terms: -4 + 4 = 0 0 + y = -4.898979486 + 4 y = -4.898979486 + 4 Combine like terms: -4.898979486 + 4 = -0.898979486 y = -0.898979486 Simplifying y = -0.898979486Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.898979486, -0.898979486}
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