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Simplifying y2 + -14y + -39 = 0 Reorder the terms: -39 + -14y + y2 = 0 Solving -39 + -14y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '39' to each side of the equation. -39 + -14y + 39 + y2 = 0 + 39 Reorder the terms: -39 + 39 + -14y + y2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + -14y + y2 = 0 + 39 -14y + y2 = 0 + 39 Combine like terms: 0 + 39 = 39 -14y + y2 = 39 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 = 39 + 49 Reorder the terms: 49 + -14y + y2 = 39 + 49 Combine like terms: 39 + 49 = 88 49 + -14y + y2 = 88 Factor a perfect square on the left side: (y + -7)(y + -7) = 88 Calculate the square root of the right side: 9.38083152 Break this problem into two subproblems by setting (y + -7) equal to 9.38083152 and -9.38083152.Subproblem 1
y + -7 = 9.38083152 Simplifying y + -7 = 9.38083152 Reorder the terms: -7 + y = 9.38083152 Solving -7 + y = 9.38083152 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 = 9.38083152 + 7 Combine like terms: -7 + 7 = 0 0 + y = 9.38083152 + 7 y = 9.38083152 + 7 Combine like terms: 9.38083152 + 7 = 16.38083152 y = 16.38083152 Simplifying y = 16.38083152Subproblem 2
y + -7 = -9.38083152 Simplifying y + -7 = -9.38083152 Reorder the terms: -7 + y = -9.38083152 Solving -7 + y = -9.38083152 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 = -9.38083152 + 7 Combine like terms: -7 + 7 = 0 0 + y = -9.38083152 + 7 y = -9.38083152 + 7 Combine like terms: -9.38083152 + 7 = -2.38083152 y = -2.38083152 Simplifying y = -2.38083152Solution
The solution to the problem is based on the solutions from the subproblems. y = {16.38083152, -2.38083152}
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