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Simplifying y2 + 8y = 45 Reorder the terms: 8y + y2 = 45 Solving 8y + y2 = 45 Solving for variable 'y'. Reorder the terms: -45 + 8y + y2 = 45 + -45 Combine like terms: 45 + -45 = 0 -45 + 8y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + 8y + 45 + y2 = 0 + 45 Reorder the terms: -45 + 45 + 8y + y2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 8y + y2 = 0 + 45 8y + y2 = 0 + 45 Combine like terms: 0 + 45 = 45 8y + y2 = 45 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 = 45 + 16 Reorder the terms: 16 + 8y + y2 = 45 + 16 Combine like terms: 45 + 16 = 61 16 + 8y + y2 = 61 Factor a perfect square on the left side: (y + 4)(y + 4) = 61 Calculate the square root of the right side: 7.810249676 Break this problem into two subproblems by setting (y + 4) equal to 7.810249676 and -7.810249676.Subproblem 1
y + 4 = 7.810249676 Simplifying y + 4 = 7.810249676 Reorder the terms: 4 + y = 7.810249676 Solving 4 + y = 7.810249676 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 = 7.810249676 + -4 Combine like terms: 4 + -4 = 0 0 + y = 7.810249676 + -4 y = 7.810249676 + -4 Combine like terms: 7.810249676 + -4 = 3.810249676 y = 3.810249676 Simplifying y = 3.810249676Subproblem 2
y + 4 = -7.810249676 Simplifying y + 4 = -7.810249676 Reorder the terms: 4 + y = -7.810249676 Solving 4 + y = -7.810249676 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 = -7.810249676 + -4 Combine like terms: 4 + -4 = 0 0 + y = -7.810249676 + -4 y = -7.810249676 + -4 Combine like terms: -7.810249676 + -4 = -11.810249676 y = -11.810249676 Simplifying y = -11.810249676Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.810249676, -11.810249676}
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