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Simplifying y2 + -4y + -71 = 0 Reorder the terms: -71 + -4y + y2 = 0 Solving -71 + -4y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '71' to each side of the equation. -71 + -4y + 71 + y2 = 0 + 71 Reorder the terms: -71 + 71 + -4y + y2 = 0 + 71 Combine like terms: -71 + 71 = 0 0 + -4y + y2 = 0 + 71 -4y + y2 = 0 + 71 Combine like terms: 0 + 71 = 71 -4y + y2 = 71 The y term is -4y. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4y + 4 + y2 = 71 + 4 Reorder the terms: 4 + -4y + y2 = 71 + 4 Combine like terms: 71 + 4 = 75 4 + -4y + y2 = 75 Factor a perfect square on the left side: (y + -2)(y + -2) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (y + -2) equal to 8.660254038 and -8.660254038.Subproblem 1
y + -2 = 8.660254038 Simplifying y + -2 = 8.660254038 Reorder the terms: -2 + y = 8.660254038 Solving -2 + y = 8.660254038 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = 8.660254038 + 2 Combine like terms: -2 + 2 = 0 0 + y = 8.660254038 + 2 y = 8.660254038 + 2 Combine like terms: 8.660254038 + 2 = 10.660254038 y = 10.660254038 Simplifying y = 10.660254038Subproblem 2
y + -2 = -8.660254038 Simplifying y + -2 = -8.660254038 Reorder the terms: -2 + y = -8.660254038 Solving -2 + y = -8.660254038 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = -8.660254038 + 2 Combine like terms: -2 + 2 = 0 0 + y = -8.660254038 + 2 y = -8.660254038 + 2 Combine like terms: -8.660254038 + 2 = -6.660254038 y = -6.660254038 Simplifying y = -6.660254038Solution
The solution to the problem is based on the solutions from the subproblems. y = {10.660254038, -6.660254038}
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