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Simplifying (2y + -7)(2y + -7) = 12 Reorder the terms: (-7 + 2y)(2y + -7) = 12 Reorder the terms: (-7 + 2y)(-7 + 2y) = 12 Multiply (-7 + 2y) * (-7 + 2y) (-7(-7 + 2y) + 2y * (-7 + 2y)) = 12 ((-7 * -7 + 2y * -7) + 2y * (-7 + 2y)) = 12 ((49 + -14y) + 2y * (-7 + 2y)) = 12 (49 + -14y + (-7 * 2y + 2y * 2y)) = 12 (49 + -14y + (-14y + 4y2)) = 12 Combine like terms: -14y + -14y = -28y (49 + -28y + 4y2) = 12 Solving 49 + -28y + 4y2 = 12 Solving for variable 'y'. Reorder the terms: 49 + -12 + -28y + 4y2 = 12 + -12 Combine like terms: 49 + -12 = 37 37 + -28y + 4y2 = 12 + -12 Combine like terms: 12 + -12 = 0 37 + -28y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 9.25 + -7y + y2 = 0 Move the constant term to the right: Add '-9.25' to each side of the equation. 9.25 + -7y + -9.25 + y2 = 0 + -9.25 Reorder the terms: 9.25 + -9.25 + -7y + y2 = 0 + -9.25 Combine like terms: 9.25 + -9.25 = 0.00 0.00 + -7y + y2 = 0 + -9.25 -7y + y2 = 0 + -9.25 Combine like terms: 0 + -9.25 = -9.25 -7y + y2 = -9.25 The y term is -7y. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7y + 12.25 + y2 = -9.25 + 12.25 Reorder the terms: 12.25 + -7y + y2 = -9.25 + 12.25 Combine like terms: -9.25 + 12.25 = 3 12.25 + -7y + y2 = 3 Factor a perfect square on the left side: (y + -3.5)(y + -3.5) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (y + -3.5) equal to 1.732050808 and -1.732050808.Subproblem 1
y + -3.5 = 1.732050808 Simplifying y + -3.5 = 1.732050808 Reorder the terms: -3.5 + y = 1.732050808 Solving -3.5 + y = 1.732050808 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + y = 1.732050808 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + y = 1.732050808 + 3.5 y = 1.732050808 + 3.5 Combine like terms: 1.732050808 + 3.5 = 5.232050808 y = 5.232050808 Simplifying y = 5.232050808Subproblem 2
y + -3.5 = -1.732050808 Simplifying y + -3.5 = -1.732050808 Reorder the terms: -3.5 + y = -1.732050808 Solving -3.5 + y = -1.732050808 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + y = -1.732050808 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + y = -1.732050808 + 3.5 y = -1.732050808 + 3.5 Combine like terms: -1.732050808 + 3.5 = 1.767949192 y = 1.767949192 Simplifying y = 1.767949192Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.232050808, 1.767949192}
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