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Simplifying y2 + -13y + 20 = 0 Reorder the terms: 20 + -13y + y2 = 0 Solving 20 + -13y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + -13y + -20 + y2 = 0 + -20 Reorder the terms: 20 + -20 + -13y + y2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -13y + y2 = 0 + -20 -13y + y2 = 0 + -20 Combine like terms: 0 + -20 = -20 -13y + y2 = -20 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 = -20 + 42.25 Reorder the terms: 42.25 + -13y + y2 = -20 + 42.25 Combine like terms: -20 + 42.25 = 22.25 42.25 + -13y + y2 = 22.25 Factor a perfect square on the left side: (y + -6.5)(y + -6.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (y + -6.5) equal to 4.716990566 and -4.716990566.Subproblem 1
y + -6.5 = 4.716990566 Simplifying y + -6.5 = 4.716990566 Reorder the terms: -6.5 + y = 4.716990566 Solving -6.5 + y = 4.716990566 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 = 4.716990566 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + y = 4.716990566 + 6.5 y = 4.716990566 + 6.5 Combine like terms: 4.716990566 + 6.5 = 11.216990566 y = 11.216990566 Simplifying y = 11.216990566Subproblem 2
y + -6.5 = -4.716990566 Simplifying y + -6.5 = -4.716990566 Reorder the terms: -6.5 + y = -4.716990566 Solving -6.5 + y = -4.716990566 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 = -4.716990566 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + y = -4.716990566 + 6.5 y = -4.716990566 + 6.5 Combine like terms: -4.716990566 + 6.5 = 1.783009434 y = 1.783009434 Simplifying y = 1.783009434Solution
The solution to the problem is based on the solutions from the subproblems. y = {11.216990566, 1.783009434}
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