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Simplifying y2 + -23y + 118 = 0 Reorder the terms: 118 + -23y + y2 = 0 Solving 118 + -23y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-118' to each side of the equation. 118 + -23y + -118 + y2 = 0 + -118 Reorder the terms: 118 + -118 + -23y + y2 = 0 + -118 Combine like terms: 118 + -118 = 0 0 + -23y + y2 = 0 + -118 -23y + y2 = 0 + -118 Combine like terms: 0 + -118 = -118 -23y + y2 = -118 The y term is -23y. Take half its coefficient (-11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. -23y + 132.25 + y2 = -118 + 132.25 Reorder the terms: 132.25 + -23y + y2 = -118 + 132.25 Combine like terms: -118 + 132.25 = 14.25 132.25 + -23y + y2 = 14.25 Factor a perfect square on the left side: (y + -11.5)(y + -11.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (y + -11.5) equal to 3.774917218 and -3.774917218.Subproblem 1
y + -11.5 = 3.774917218 Simplifying y + -11.5 = 3.774917218 Reorder the terms: -11.5 + y = 3.774917218 Solving -11.5 + y = 3.774917218 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + y = 3.774917218 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + y = 3.774917218 + 11.5 y = 3.774917218 + 11.5 Combine like terms: 3.774917218 + 11.5 = 15.274917218 y = 15.274917218 Simplifying y = 15.274917218Subproblem 2
y + -11.5 = -3.774917218 Simplifying y + -11.5 = -3.774917218 Reorder the terms: -11.5 + y = -3.774917218 Solving -11.5 + y = -3.774917218 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + y = -3.774917218 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + y = -3.774917218 + 11.5 y = -3.774917218 + 11.5 Combine like terms: -3.774917218 + 11.5 = 7.725082782 y = 7.725082782 Simplifying y = 7.725082782Solution
The solution to the problem is based on the solutions from the subproblems. y = {15.274917218, 7.725082782}
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