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Simplifying y2 + -22y + 24 = 0 Reorder the terms: 24 + -22y + y2 = 0 Solving 24 + -22y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + -22y + -24 + y2 = 0 + -24 Reorder the terms: 24 + -24 + -22y + y2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -22y + y2 = 0 + -24 -22y + y2 = 0 + -24 Combine like terms: 0 + -24 = -24 -22y + y2 = -24 The y term is -22y. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22y + 121 + y2 = -24 + 121 Reorder the terms: 121 + -22y + y2 = -24 + 121 Combine like terms: -24 + 121 = 97 121 + -22y + y2 = 97 Factor a perfect square on the left side: (y + -11)(y + -11) = 97 Calculate the square root of the right side: 9.848857802 Break this problem into two subproblems by setting (y + -11) equal to 9.848857802 and -9.848857802.Subproblem 1
y + -11 = 9.848857802 Simplifying y + -11 = 9.848857802 Reorder the terms: -11 + y = 9.848857802 Solving -11 + y = 9.848857802 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + y = 9.848857802 + 11 Combine like terms: -11 + 11 = 0 0 + y = 9.848857802 + 11 y = 9.848857802 + 11 Combine like terms: 9.848857802 + 11 = 20.848857802 y = 20.848857802 Simplifying y = 20.848857802Subproblem 2
y + -11 = -9.848857802 Simplifying y + -11 = -9.848857802 Reorder the terms: -11 + y = -9.848857802 Solving -11 + y = -9.848857802 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + y = -9.848857802 + 11 Combine like terms: -11 + 11 = 0 0 + y = -9.848857802 + 11 y = -9.848857802 + 11 Combine like terms: -9.848857802 + 11 = 1.151142198 y = 1.151142198 Simplifying y = 1.151142198Solution
The solution to the problem is based on the solutions from the subproblems. y = {20.848857802, 1.151142198}
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