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Simplifying y2 + 7y + -14 = 0 Reorder the terms: -14 + 7y + y2 = 0 Solving -14 + 7y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + 7y + 14 + y2 = 0 + 14 Reorder the terms: -14 + 14 + 7y + y2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 7y + y2 = 0 + 14 7y + y2 = 0 + 14 Combine like terms: 0 + 14 = 14 7y + y2 = 14 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 = 14 + 12.25 Reorder the terms: 12.25 + 7y + y2 = 14 + 12.25 Combine like terms: 14 + 12.25 = 26.25 12.25 + 7y + y2 = 26.25 Factor a perfect square on the left side: (y + 3.5)(y + 3.5) = 26.25 Calculate the square root of the right side: 5.123475383 Break this problem into two subproblems by setting (y + 3.5) equal to 5.123475383 and -5.123475383.Subproblem 1
y + 3.5 = 5.123475383 Simplifying y + 3.5 = 5.123475383 Reorder the terms: 3.5 + y = 5.123475383 Solving 3.5 + y = 5.123475383 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 = 5.123475383 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + y = 5.123475383 + -3.5 y = 5.123475383 + -3.5 Combine like terms: 5.123475383 + -3.5 = 1.623475383 y = 1.623475383 Simplifying y = 1.623475383Subproblem 2
y + 3.5 = -5.123475383 Simplifying y + 3.5 = -5.123475383 Reorder the terms: 3.5 + y = -5.123475383 Solving 3.5 + y = -5.123475383 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 = -5.123475383 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + y = -5.123475383 + -3.5 y = -5.123475383 + -3.5 Combine like terms: -5.123475383 + -3.5 = -8.623475383 y = -8.623475383 Simplifying y = -8.623475383Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.623475383, -8.623475383}
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