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Simplifying y2 + -11y + 7 = 0 Reorder the terms: 7 + -11y + y2 = 0 Solving 7 + -11y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + -11y + -7 + y2 = 0 + -7 Reorder the terms: 7 + -7 + -11y + y2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -11y + y2 = 0 + -7 -11y + y2 = 0 + -7 Combine like terms: 0 + -7 = -7 -11y + y2 = -7 The y term is -11y. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11y + 30.25 + y2 = -7 + 30.25 Reorder the terms: 30.25 + -11y + y2 = -7 + 30.25 Combine like terms: -7 + 30.25 = 23.25 30.25 + -11y + y2 = 23.25 Factor a perfect square on the left side: (y + -5.5)(y + -5.5) = 23.25 Calculate the square root of the right side: 4.82182538 Break this problem into two subproblems by setting (y + -5.5) equal to 4.82182538 and -4.82182538.Subproblem 1
y + -5.5 = 4.82182538 Simplifying y + -5.5 = 4.82182538 Reorder the terms: -5.5 + y = 4.82182538 Solving -5.5 + y = 4.82182538 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + y = 4.82182538 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + y = 4.82182538 + 5.5 y = 4.82182538 + 5.5 Combine like terms: 4.82182538 + 5.5 = 10.32182538 y = 10.32182538 Simplifying y = 10.32182538Subproblem 2
y + -5.5 = -4.82182538 Simplifying y + -5.5 = -4.82182538 Reorder the terms: -5.5 + y = -4.82182538 Solving -5.5 + y = -4.82182538 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + y = -4.82182538 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + y = -4.82182538 + 5.5 y = -4.82182538 + 5.5 Combine like terms: -4.82182538 + 5.5 = 0.67817462 y = 0.67817462 Simplifying y = 0.67817462Solution
The solution to the problem is based on the solutions from the subproblems. y = {10.32182538, 0.67817462}
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