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Simplifying y2 + 13y + -36 = 0 Reorder the terms: -36 + 13y + y2 = 0 Solving -36 + 13y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + 13y + 36 + y2 = 0 + 36 Reorder the terms: -36 + 36 + 13y + y2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 13y + y2 = 0 + 36 13y + y2 = 0 + 36 Combine like terms: 0 + 36 = 36 13y + y2 = 36 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 = 36 + 42.25 Reorder the terms: 42.25 + 13y + y2 = 36 + 42.25 Combine like terms: 36 + 42.25 = 78.25 42.25 + 13y + y2 = 78.25 Factor a perfect square on the left side: (y + 6.5)(y + 6.5) = 78.25 Calculate the square root of the right side: 8.845903006 Break this problem into two subproblems by setting (y + 6.5) equal to 8.845903006 and -8.845903006.Subproblem 1
y + 6.5 = 8.845903006 Simplifying y + 6.5 = 8.845903006 Reorder the terms: 6.5 + y = 8.845903006 Solving 6.5 + y = 8.845903006 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 = 8.845903006 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + y = 8.845903006 + -6.5 y = 8.845903006 + -6.5 Combine like terms: 8.845903006 + -6.5 = 2.345903006 y = 2.345903006 Simplifying y = 2.345903006Subproblem 2
y + 6.5 = -8.845903006 Simplifying y + 6.5 = -8.845903006 Reorder the terms: 6.5 + y = -8.845903006 Solving 6.5 + y = -8.845903006 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 = -8.845903006 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + y = -8.845903006 + -6.5 y = -8.845903006 + -6.5 Combine like terms: -8.845903006 + -6.5 = -15.345903006 y = -15.345903006 Simplifying y = -15.345903006Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.345903006, -15.345903006}
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