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Simplifying y(y) + -26y + 28 = 0 Multiply y * y y2 + -26y + 28 = 0 Reorder the terms: 28 + -26y + y2 = 0 Solving 28 + -26y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-28' to each side of the equation. 28 + -26y + -28 + y2 = 0 + -28 Reorder the terms: 28 + -28 + -26y + y2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + -26y + y2 = 0 + -28 -26y + y2 = 0 + -28 Combine like terms: 0 + -28 = -28 -26y + y2 = -28 The y term is -26y. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26y + 169 + y2 = -28 + 169 Reorder the terms: 169 + -26y + y2 = -28 + 169 Combine like terms: -28 + 169 = 141 169 + -26y + y2 = 141 Factor a perfect square on the left side: (y + -13)(y + -13) = 141 Calculate the square root of the right side: 11.874342087 Break this problem into two subproblems by setting (y + -13) equal to 11.874342087 and -11.874342087.Subproblem 1
y + -13 = 11.874342087 Simplifying y + -13 = 11.874342087 Reorder the terms: -13 + y = 11.874342087 Solving -13 + y = 11.874342087 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + y = 11.874342087 + 13 Combine like terms: -13 + 13 = 0 0 + y = 11.874342087 + 13 y = 11.874342087 + 13 Combine like terms: 11.874342087 + 13 = 24.874342087 y = 24.874342087 Simplifying y = 24.874342087Subproblem 2
y + -13 = -11.874342087 Simplifying y + -13 = -11.874342087 Reorder the terms: -13 + y = -11.874342087 Solving -13 + y = -11.874342087 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + y = -11.874342087 + 13 Combine like terms: -13 + 13 = 0 0 + y = -11.874342087 + 13 y = -11.874342087 + 13 Combine like terms: -11.874342087 + 13 = 1.125657913 y = 1.125657913 Simplifying y = 1.125657913Solution
The solution to the problem is based on the solutions from the subproblems. y = {24.874342087, 1.125657913}
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