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Simplifying 2y2 + -28 + -7y = y2 + -4 Reorder the terms: -28 + -7y + 2y2 = y2 + -4 Reorder the terms: -28 + -7y + 2y2 = -4 + y2 Solving -28 + -7y + 2y2 = -4 + y2 Solving for variable 'y'. Reorder the terms: -28 + 4 + -7y + 2y2 + -1y2 = -4 + y2 + 4 + -1y2 Combine like terms: -28 + 4 = -24 -24 + -7y + 2y2 + -1y2 = -4 + y2 + 4 + -1y2 Combine like terms: 2y2 + -1y2 = 1y2 -24 + -7y + 1y2 = -4 + y2 + 4 + -1y2 Reorder the terms: -24 + -7y + 1y2 = -4 + 4 + y2 + -1y2 Combine like terms: -4 + 4 = 0 -24 + -7y + 1y2 = 0 + y2 + -1y2 -24 + -7y + 1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -24 + -7y + 1y2 = 0 Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + -7y + 24 + y2 = 0 + 24 Reorder the terms: -24 + 24 + -7y + y2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -7y + y2 = 0 + 24 -7y + y2 = 0 + 24 Combine like terms: 0 + 24 = 24 -7y + y2 = 24 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 = 24 + 12.25 Reorder the terms: 12.25 + -7y + y2 = 24 + 12.25 Combine like terms: 24 + 12.25 = 36.25 12.25 + -7y + y2 = 36.25 Factor a perfect square on the left side: (y + -3.5)(y + -3.5) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (y + -3.5) equal to 6.020797289 and -6.020797289.Subproblem 1
y + -3.5 = 6.020797289 Simplifying y + -3.5 = 6.020797289 Reorder the terms: -3.5 + y = 6.020797289 Solving -3.5 + y = 6.020797289 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 = 6.020797289 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + y = 6.020797289 + 3.5 y = 6.020797289 + 3.5 Combine like terms: 6.020797289 + 3.5 = 9.520797289 y = 9.520797289 Simplifying y = 9.520797289Subproblem 2
y + -3.5 = -6.020797289 Simplifying y + -3.5 = -6.020797289 Reorder the terms: -3.5 + y = -6.020797289 Solving -3.5 + y = -6.020797289 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 = -6.020797289 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + y = -6.020797289 + 3.5 y = -6.020797289 + 3.5 Combine like terms: -6.020797289 + 3.5 = -2.520797289 y = -2.520797289 Simplifying y = -2.520797289Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.520797289, -2.520797289}
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