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Simplifying (y + -7)(y + -7) + -12 = 0 Reorder the terms: (-7 + y)(y + -7) + -12 = 0 Reorder the terms: (-7 + y)(-7 + y) + -12 = 0 Multiply (-7 + y) * (-7 + y) (-7(-7 + y) + y(-7 + y)) + -12 = 0 ((-7 * -7 + y * -7) + y(-7 + y)) + -12 = 0 ((49 + -7y) + y(-7 + y)) + -12 = 0 (49 + -7y + (-7 * y + y * y)) + -12 = 0 (49 + -7y + (-7y + y2)) + -12 = 0 Combine like terms: -7y + -7y = -14y (49 + -14y + y2) + -12 = 0 Reorder the terms: 49 + -12 + -14y + y2 = 0 Combine like terms: 49 + -12 = 37 37 + -14y + y2 = 0 Solving 37 + -14y + y2 = 0 Solving for variable 'y'. 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 = 10.464101615 y = 10.464101615 Simplifying y = 10.464101615Subproblem 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 = 3.535898385 y = 3.535898385 Simplifying y = 3.535898385Solution
The solution to the problem is based on the solutions from the subproblems. y = {10.464101615, 3.535898385}
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