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Simplifying y2 + -14y + 15 = 0 Reorder the terms: 15 + -14y + y2 = 0 Solving 15 + -14y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + -14y + -15 + y2 = 0 + -15 Reorder the terms: 15 + -15 + -14y + y2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -14y + y2 = 0 + -15 -14y + y2 = 0 + -15 Combine like terms: 0 + -15 = -15 -14y + y2 = -15 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 = -15 + 49 Reorder the terms: 49 + -14y + y2 = -15 + 49 Combine like terms: -15 + 49 = 34 49 + -14y + y2 = 34 Factor a perfect square on the left side: (y + -7)(y + -7) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (y + -7) equal to 5.830951895 and -5.830951895.Subproblem 1
y + -7 = 5.830951895 Simplifying y + -7 = 5.830951895 Reorder the terms: -7 + y = 5.830951895 Solving -7 + y = 5.830951895 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 = 5.830951895 + 7 Combine like terms: -7 + 7 = 0 0 + y = 5.830951895 + 7 y = 5.830951895 + 7 Combine like terms: 5.830951895 + 7 = 12.830951895 y = 12.830951895 Simplifying y = 12.830951895Subproblem 2
y + -7 = -5.830951895 Simplifying y + -7 = -5.830951895 Reorder the terms: -7 + y = -5.830951895 Solving -7 + y = -5.830951895 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 = -5.830951895 + 7 Combine like terms: -7 + 7 = 0 0 + y = -5.830951895 + 7 y = -5.830951895 + 7 Combine like terms: -5.830951895 + 7 = 1.169048105 y = 1.169048105 Simplifying y = 1.169048105Solution
The solution to the problem is based on the solutions from the subproblems. y = {12.830951895, 1.169048105}
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