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Simplifying y2 + -14y + 22 = 0 Reorder the terms: 22 + -14y + y2 = 0 Solving 22 + -14y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-22' to each side of the equation. 22 + -14y + -22 + y2 = 0 + -22 Reorder the terms: 22 + -22 + -14y + y2 = 0 + -22 Combine like terms: 22 + -22 = 0 0 + -14y + y2 = 0 + -22 -14y + y2 = 0 + -22 Combine like terms: 0 + -22 = -22 -14y + y2 = -22 The y term is -14y. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14y + 49 + y2 = -22 + 49 Reorder the terms: 49 + -14y + y2 = -22 + 49 Combine like terms: -22 + 49 = 27 49 + -14y + y2 = 27 Factor a perfect square on the left side: (y + -7)(y + -7) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (y + -7) equal to 5.196152423 and -5.196152423.Subproblem 1
y + -7 = 5.196152423 Simplifying y + -7 = 5.196152423 Reorder the terms: -7 + y = 5.196152423 Solving -7 + y = 5.196152423 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + y = 5.196152423 + 7 Combine like terms: -7 + 7 = 0 0 + y = 5.196152423 + 7 y = 5.196152423 + 7 Combine like terms: 5.196152423 + 7 = 12.196152423 y = 12.196152423 Simplifying y = 12.196152423Subproblem 2
y + -7 = -5.196152423 Simplifying y + -7 = -5.196152423 Reorder the terms: -7 + y = -5.196152423 Solving -7 + y = -5.196152423 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + y = -5.196152423 + 7 Combine like terms: -7 + 7 = 0 0 + y = -5.196152423 + 7 y = -5.196152423 + 7 Combine like terms: -5.196152423 + 7 = 1.803847577 y = 1.803847577 Simplifying y = 1.803847577Solution
The solution to the problem is based on the solutions from the subproblems. y = {12.196152423, 1.803847577}
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