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Simplifying y2 + -14y = 26 Reorder the terms: -14y + y2 = 26 Solving -14y + y2 = 26 Solving for variable 'y'. Reorder the terms: -26 + -14y + y2 = 26 + -26 Combine like terms: 26 + -26 = 0 -26 + -14y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '26' to each side of the equation. -26 + -14y + 26 + y2 = 0 + 26 Reorder the terms: -26 + 26 + -14y + y2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + -14y + y2 = 0 + 26 -14y + y2 = 0 + 26 Combine like terms: 0 + 26 = 26 -14y + y2 = 26 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 = 26 + 49 Reorder the terms: 49 + -14y + y2 = 26 + 49 Combine like terms: 26 + 49 = 75 49 + -14y + y2 = 75 Factor a perfect square on the left side: (y + -7)(y + -7) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (y + -7) equal to 8.660254038 and -8.660254038.Subproblem 1
y + -7 = 8.660254038 Simplifying y + -7 = 8.660254038 Reorder the terms: -7 + y = 8.660254038 Solving -7 + y = 8.660254038 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 = 8.660254038 + 7 Combine like terms: -7 + 7 = 0 0 + y = 8.660254038 + 7 y = 8.660254038 + 7 Combine like terms: 8.660254038 + 7 = 15.660254038 y = 15.660254038 Simplifying y = 15.660254038Subproblem 2
y + -7 = -8.660254038 Simplifying y + -7 = -8.660254038 Reorder the terms: -7 + y = -8.660254038 Solving -7 + y = -8.660254038 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 = -8.660254038 + 7 Combine like terms: -7 + 7 = 0 0 + y = -8.660254038 + 7 y = -8.660254038 + 7 Combine like terms: -8.660254038 + 7 = -1.660254038 y = -1.660254038 Simplifying y = -1.660254038Solution
The solution to the problem is based on the solutions from the subproblems. y = {15.660254038, -1.660254038}
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