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Simplifying y2 + 14y + 49 = 12 Reorder the terms: 49 + 14y + y2 = 12 Solving 49 + 14y + y2 = 12 Solving for variable 'y'. Reorder the terms: 49 + -12 + 14y + y2 = 12 + -12 Combine like terms: 49 + -12 = 37 37 + 14y + y2 = 12 + -12 Combine like terms: 12 + -12 = 0 37 + 14y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-37' to each side of the equation. 37 + 14y + -37 + y2 = 0 + -37 Reorder the terms: 37 + -37 + 14y + y2 = 0 + -37 Combine like terms: 37 + -37 = 0 0 + 14y + y2 = 0 + -37 14y + y2 = 0 + -37 Combine like terms: 0 + -37 = -37 14y + y2 = -37 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 = -37 + 49 Reorder the terms: 49 + 14y + y2 = -37 + 49 Combine like terms: -37 + 49 = 12 49 + 14y + y2 = 12 Factor a perfect square on the left side: (y + 7)(y + 7) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (y + 7) equal to 3.464101615 and -3.464101615.Subproblem 1
y + 7 = 3.464101615 Simplifying y + 7 = 3.464101615 Reorder the terms: 7 + y = 3.464101615 Solving 7 + y = 3.464101615 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 = 3.464101615 + -7 Combine like terms: 7 + -7 = 0 0 + y = 3.464101615 + -7 y = 3.464101615 + -7 Combine like terms: 3.464101615 + -7 = -3.535898385 y = -3.535898385 Simplifying y = -3.535898385Subproblem 2
y + 7 = -3.464101615 Simplifying y + 7 = -3.464101615 Reorder the terms: 7 + y = -3.464101615 Solving 7 + y = -3.464101615 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 = -3.464101615 + -7 Combine like terms: 7 + -7 = 0 0 + y = -3.464101615 + -7 y = -3.464101615 + -7 Combine like terms: -3.464101615 + -7 = -10.464101615 y = -10.464101615 Simplifying y = -10.464101615Solution
The solution to the problem is based on the solutions from the subproblems. y = {-3.535898385, -10.464101615}
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