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Simplifying y2 + 8y = 3 Reorder the terms: 8y + y2 = 3 Solving 8y + y2 = 3 Solving for variable 'y'. Reorder the terms: -3 + 8y + y2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 8y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 8y + 3 + y2 = 0 + 3 Reorder the terms: -3 + 3 + 8y + y2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 8y + y2 = 0 + 3 8y + y2 = 0 + 3 Combine like terms: 0 + 3 = 3 8y + y2 = 3 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 = 3 + 16 Reorder the terms: 16 + 8y + y2 = 3 + 16 Combine like terms: 3 + 16 = 19 16 + 8y + y2 = 19 Factor a perfect square on the left side: (y + 4)(y + 4) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (y + 4) equal to 4.358898944 and -4.358898944.Subproblem 1
y + 4 = 4.358898944 Simplifying y + 4 = 4.358898944 Reorder the terms: 4 + y = 4.358898944 Solving 4 + y = 4.358898944 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 = 4.358898944 + -4 Combine like terms: 4 + -4 = 0 0 + y = 4.358898944 + -4 y = 4.358898944 + -4 Combine like terms: 4.358898944 + -4 = 0.358898944 y = 0.358898944 Simplifying y = 0.358898944Subproblem 2
y + 4 = -4.358898944 Simplifying y + 4 = -4.358898944 Reorder the terms: 4 + y = -4.358898944 Solving 4 + y = -4.358898944 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 = -4.358898944 + -4 Combine like terms: 4 + -4 = 0 0 + y = -4.358898944 + -4 y = -4.358898944 + -4 Combine like terms: -4.358898944 + -4 = -8.358898944 y = -8.358898944 Simplifying y = -8.358898944Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.358898944, -8.358898944}
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