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Simplifying y2 + y = 26 Reorder the terms: y + y2 = 26 Solving y + y2 = 26 Solving for variable 'y'. Reorder the terms: -26 + y + y2 = 26 + -26 Combine like terms: 26 + -26 = 0 -26 + y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '26' to each side of the equation. -26 + y + 26 + y2 = 0 + 26 Reorder the terms: -26 + 26 + y + y2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + y + y2 = 0 + 26 y + y2 = 0 + 26 Combine like terms: 0 + 26 = 26 y + y2 = 26 The y term is y. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. y + 0.25 + y2 = 26 + 0.25 Reorder the terms: 0.25 + y + y2 = 26 + 0.25 Combine like terms: 26 + 0.25 = 26.25 0.25 + y + y2 = 26.25 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = 26.25 Calculate the square root of the right side: 5.123475383 Break this problem into two subproblems by setting (y + 0.5) equal to 5.123475383 and -5.123475383.Subproblem 1
y + 0.5 = 5.123475383 Simplifying y + 0.5 = 5.123475383 Reorder the terms: 0.5 + y = 5.123475383 Solving 0.5 + y = 5.123475383 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = 5.123475383 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 5.123475383 + -0.5 y = 5.123475383 + -0.5 Combine like terms: 5.123475383 + -0.5 = 4.623475383 y = 4.623475383 Simplifying y = 4.623475383Subproblem 2
y + 0.5 = -5.123475383 Simplifying y + 0.5 = -5.123475383 Reorder the terms: 0.5 + y = -5.123475383 Solving 0.5 + y = -5.123475383 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = -5.123475383 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -5.123475383 + -0.5 y = -5.123475383 + -0.5 Combine like terms: -5.123475383 + -0.5 = -5.623475383 y = -5.623475383 Simplifying y = -5.623475383Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.623475383, -5.623475383}
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