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Simplifying 12 = y2 + -8y + -16 Reorder the terms: 12 = -16 + -8y + y2 Solving 12 = -16 + -8y + y2 Solving for variable 'y'. Combine like terms: 12 + 16 = 28 28 + 8y + -1y2 = -16 + -8y + y2 + 16 + 8y + -1y2 Reorder the terms: 28 + 8y + -1y2 = -16 + 16 + -8y + 8y + y2 + -1y2 Combine like terms: -16 + 16 = 0 28 + 8y + -1y2 = 0 + -8y + 8y + y2 + -1y2 28 + 8y + -1y2 = -8y + 8y + y2 + -1y2 Combine like terms: -8y + 8y = 0 28 + 8y + -1y2 = 0 + y2 + -1y2 28 + 8y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 28 + 8y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -28 + -8y + y2 = 0 Move the constant term to the right: Add '28' to each side of the equation. -28 + -8y + 28 + y2 = 0 + 28 Reorder the terms: -28 + 28 + -8y + y2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -8y + y2 = 0 + 28 -8y + y2 = 0 + 28 Combine like terms: 0 + 28 = 28 -8y + y2 = 28 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 = 28 + 16 Reorder the terms: 16 + -8y + y2 = 28 + 16 Combine like terms: 28 + 16 = 44 16 + -8y + y2 = 44 Factor a perfect square on the left side: (y + -4)(y + -4) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (y + -4) equal to 6.633249581 and -6.633249581.Subproblem 1
y + -4 = 6.633249581 Simplifying y + -4 = 6.633249581 Reorder the terms: -4 + y = 6.633249581 Solving -4 + y = 6.633249581 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 = 6.633249581 + 4 Combine like terms: -4 + 4 = 0 0 + y = 6.633249581 + 4 y = 6.633249581 + 4 Combine like terms: 6.633249581 + 4 = 10.633249581 y = 10.633249581 Simplifying y = 10.633249581Subproblem 2
y + -4 = -6.633249581 Simplifying y + -4 = -6.633249581 Reorder the terms: -4 + y = -6.633249581 Solving -4 + y = -6.633249581 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 = -6.633249581 + 4 Combine like terms: -4 + 4 = 0 0 + y = -6.633249581 + 4 y = -6.633249581 + 4 Combine like terms: -6.633249581 + 4 = -2.633249581 y = -2.633249581 Simplifying y = -2.633249581Solution
The solution to the problem is based on the solutions from the subproblems. y = {10.633249581, -2.633249581}
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