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Simplifying y2 + 13 = 8y Reorder the terms: 13 + y2 = 8y Solving 13 + y2 = 8y Solving for variable 'y'. Reorder the terms: 13 + -8y + y2 = 8y + -8y Combine like terms: 8y + -8y = 0 13 + -8y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + -8y + -13 + y2 = 0 + -13 Reorder the terms: 13 + -13 + -8y + y2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -8y + y2 = 0 + -13 -8y + y2 = 0 + -13 Combine like terms: 0 + -13 = -13 -8y + y2 = -13 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 = -13 + 16 Reorder the terms: 16 + -8y + y2 = -13 + 16 Combine like terms: -13 + 16 = 3 16 + -8y + y2 = 3 Factor a perfect square on the left side: (y + -4)(y + -4) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (y + -4) equal to 1.732050808 and -1.732050808.Subproblem 1
y + -4 = 1.732050808 Simplifying y + -4 = 1.732050808 Reorder the terms: -4 + y = 1.732050808 Solving -4 + y = 1.732050808 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 = 1.732050808 + 4 Combine like terms: -4 + 4 = 0 0 + y = 1.732050808 + 4 y = 1.732050808 + 4 Combine like terms: 1.732050808 + 4 = 5.732050808 y = 5.732050808 Simplifying y = 5.732050808Subproblem 2
y + -4 = -1.732050808 Simplifying y + -4 = -1.732050808 Reorder the terms: -4 + y = -1.732050808 Solving -4 + y = -1.732050808 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 = -1.732050808 + 4 Combine like terms: -4 + 4 = 0 0 + y = -1.732050808 + 4 y = -1.732050808 + 4 Combine like terms: -1.732050808 + 4 = 2.267949192 y = 2.267949192 Simplifying y = 2.267949192Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.732050808, 2.267949192}
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