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Simplifying y2 + -14y + -35 = 0 Reorder the terms: -35 + -14y + y2 = 0 Solving -35 + -14y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + -14y + 35 + y2 = 0 + 35 Reorder the terms: -35 + 35 + -14y + y2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -14y + y2 = 0 + 35 -14y + y2 = 0 + 35 Combine like terms: 0 + 35 = 35 -14y + y2 = 35 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 = 35 + 49 Reorder the terms: 49 + -14y + y2 = 35 + 49 Combine like terms: 35 + 49 = 84 49 + -14y + y2 = 84 Factor a perfect square on the left side: (y + -7)(y + -7) = 84 Calculate the square root of the right side: 9.16515139 Break this problem into two subproblems by setting (y + -7) equal to 9.16515139 and -9.16515139.Subproblem 1
y + -7 = 9.16515139 Simplifying y + -7 = 9.16515139 Reorder the terms: -7 + y = 9.16515139 Solving -7 + y = 9.16515139 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 = 9.16515139 + 7 Combine like terms: -7 + 7 = 0 0 + y = 9.16515139 + 7 y = 9.16515139 + 7 Combine like terms: 9.16515139 + 7 = 16.16515139 y = 16.16515139 Simplifying y = 16.16515139Subproblem 2
y + -7 = -9.16515139 Simplifying y + -7 = -9.16515139 Reorder the terms: -7 + y = -9.16515139 Solving -7 + y = -9.16515139 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 = -9.16515139 + 7 Combine like terms: -7 + 7 = 0 0 + y = -9.16515139 + 7 y = -9.16515139 + 7 Combine like terms: -9.16515139 + 7 = -2.16515139 y = -2.16515139 Simplifying y = -2.16515139Solution
The solution to the problem is based on the solutions from the subproblems. y = {16.16515139, -2.16515139}
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