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Simplifying y2 = 13y + 1 Reorder the terms: y2 = 1 + 13y Solving y2 = 1 + 13y Solving for variable 'y'. Reorder the terms: -1 + -13y + y2 = 1 + 13y + -1 + -13y Reorder the terms: -1 + -13y + y2 = 1 + -1 + 13y + -13y Combine like terms: 1 + -1 = 0 -1 + -13y + y2 = 0 + 13y + -13y -1 + -13y + y2 = 13y + -13y Combine like terms: 13y + -13y = 0 -1 + -13y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -13y + 1 + y2 = 0 + 1 Reorder the terms: -1 + 1 + -13y + y2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -13y + y2 = 0 + 1 -13y + y2 = 0 + 1 Combine like terms: 0 + 1 = 1 -13y + y2 = 1 The y term is -13y. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13y + 42.25 + y2 = 1 + 42.25 Reorder the terms: 42.25 + -13y + y2 = 1 + 42.25 Combine like terms: 1 + 42.25 = 43.25 42.25 + -13y + y2 = 43.25 Factor a perfect square on the left side: (y + -6.5)(y + -6.5) = 43.25 Calculate the square root of the right side: 6.576473219 Break this problem into two subproblems by setting (y + -6.5) equal to 6.576473219 and -6.576473219.Subproblem 1
y + -6.5 = 6.576473219 Simplifying y + -6.5 = 6.576473219 Reorder the terms: -6.5 + y = 6.576473219 Solving -6.5 + y = 6.576473219 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + y = 6.576473219 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + y = 6.576473219 + 6.5 y = 6.576473219 + 6.5 Combine like terms: 6.576473219 + 6.5 = 13.076473219 y = 13.076473219 Simplifying y = 13.076473219Subproblem 2
y + -6.5 = -6.576473219 Simplifying y + -6.5 = -6.576473219 Reorder the terms: -6.5 + y = -6.576473219 Solving -6.5 + y = -6.576473219 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + y = -6.576473219 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + y = -6.576473219 + 6.5 y = -6.576473219 + 6.5 Combine like terms: -6.576473219 + 6.5 = -0.076473219 y = -0.076473219 Simplifying y = -0.076473219Solution
The solution to the problem is based on the solutions from the subproblems. y = {13.076473219, -0.076473219}
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