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Simplifying y2 + 14y + -36 = 0 Reorder the terms: -36 + 14y + y2 = 0 Solving -36 + 14y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + 14y + 36 + y2 = 0 + 36 Reorder the terms: -36 + 36 + 14y + y2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 14y + y2 = 0 + 36 14y + y2 = 0 + 36 Combine like terms: 0 + 36 = 36 14y + y2 = 36 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 = 36 + 49 Reorder the terms: 49 + 14y + y2 = 36 + 49 Combine like terms: 36 + 49 = 85 49 + 14y + y2 = 85 Factor a perfect square on the left side: (y + 7)(y + 7) = 85 Calculate the square root of the right side: 9.219544457 Break this problem into two subproblems by setting (y + 7) equal to 9.219544457 and -9.219544457.Subproblem 1
y + 7 = 9.219544457 Simplifying y + 7 = 9.219544457 Reorder the terms: 7 + y = 9.219544457 Solving 7 + y = 9.219544457 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 = 9.219544457 + -7 Combine like terms: 7 + -7 = 0 0 + y = 9.219544457 + -7 y = 9.219544457 + -7 Combine like terms: 9.219544457 + -7 = 2.219544457 y = 2.219544457 Simplifying y = 2.219544457Subproblem 2
y + 7 = -9.219544457 Simplifying y + 7 = -9.219544457 Reorder the terms: 7 + y = -9.219544457 Solving 7 + y = -9.219544457 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 = -9.219544457 + -7 Combine like terms: 7 + -7 = 0 0 + y = -9.219544457 + -7 y = -9.219544457 + -7 Combine like terms: -9.219544457 + -7 = -16.219544457 y = -16.219544457 Simplifying y = -16.219544457Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.219544457, -16.219544457}
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