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Simplifying y2 + 7y + -1 = 0 Reorder the terms: -1 + 7y + y2 = 0 Solving -1 + 7y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 7y + 1 + y2 = 0 + 1 Reorder the terms: -1 + 1 + 7y + y2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 7y + y2 = 0 + 1 7y + y2 = 0 + 1 Combine like terms: 0 + 1 = 1 7y + y2 = 1 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 = 1 + 12.25 Reorder the terms: 12.25 + 7y + y2 = 1 + 12.25 Combine like terms: 1 + 12.25 = 13.25 12.25 + 7y + y2 = 13.25 Factor a perfect square on the left side: (y + 3.5)(y + 3.5) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (y + 3.5) equal to 3.640054945 and -3.640054945.Subproblem 1
y + 3.5 = 3.640054945 Simplifying y + 3.5 = 3.640054945 Reorder the terms: 3.5 + y = 3.640054945 Solving 3.5 + y = 3.640054945 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 = 3.640054945 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + y = 3.640054945 + -3.5 y = 3.640054945 + -3.5 Combine like terms: 3.640054945 + -3.5 = 0.140054945 y = 0.140054945 Simplifying y = 0.140054945Subproblem 2
y + 3.5 = -3.640054945 Simplifying y + 3.5 = -3.640054945 Reorder the terms: 3.5 + y = -3.640054945 Solving 3.5 + y = -3.640054945 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 = -3.640054945 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + y = -3.640054945 + -3.5 y = -3.640054945 + -3.5 Combine like terms: -3.640054945 + -3.5 = -7.140054945 y = -7.140054945 Simplifying y = -7.140054945Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.140054945, -7.140054945}
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