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Simplifying 0 = y2 + 1y + -18 Reorder the terms: 0 = -18 + 1y + y2 Solving 0 = -18 + 1y + y2 Solving for variable 'y'. Combine like terms: 0 + 18 = 18 18 + -1y + -1y2 = -18 + 1y + y2 + 18 + -1y + -1y2 Reorder the terms: 18 + -1y + -1y2 = -18 + 18 + 1y + -1y + y2 + -1y2 Combine like terms: -18 + 18 = 0 18 + -1y + -1y2 = 0 + 1y + -1y + y2 + -1y2 18 + -1y + -1y2 = 1y + -1y + y2 + -1y2 Combine like terms: 1y + -1y = 0 18 + -1y + -1y2 = 0 + y2 + -1y2 18 + -1y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 18 + -1y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -18 + y + y2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + y + 18 + y2 = 0 + 18 Reorder the terms: -18 + 18 + y + y2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + y + y2 = 0 + 18 y + y2 = 0 + 18 Combine like terms: 0 + 18 = 18 y + y2 = 18 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. + 0.25 + y2 = 18 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + y2 = 18 + 0.25 Combine like terms: 18 + 0.25 = 18.25 1.25 + y2 = 18.25 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (y + 0.5) equal to 4.272001873 and -4.272001873.Subproblem 1
y + 0.5 = 4.272001873 Simplifying y + 0.5 = 4.272001873 Reorder the terms: 0.5 + y = 4.272001873 Solving 0.5 + y = 4.272001873 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 = 4.272001873 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 4.272001873 + -0.5 y = 4.272001873 + -0.5 Combine like terms: 4.272001873 + -0.5 = 3.772001873 y = 3.772001873 Simplifying y = 3.772001873Subproblem 2
y + 0.5 = -4.272001873 Simplifying y + 0.5 = -4.272001873 Reorder the terms: 0.5 + y = -4.272001873 Solving 0.5 + y = -4.272001873 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 = -4.272001873 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -4.272001873 + -0.5 y = -4.272001873 + -0.5 Combine like terms: -4.272001873 + -0.5 = -4.772001873 y = -4.772001873 Simplifying y = -4.772001873Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.772001873, -4.772001873}
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