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Simplifying y2 + -19y = 4 Reorder the terms: -19y + y2 = 4 Solving -19y + y2 = 4 Solving for variable 'y'. Reorder the terms: -4 + -19y + y2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + -19y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -19y + 4 + y2 = 0 + 4 Reorder the terms: -4 + 4 + -19y + y2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -19y + y2 = 0 + 4 -19y + y2 = 0 + 4 Combine like terms: 0 + 4 = 4 -19y + y2 = 4 The y term is -19y. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19y + 90.25 + y2 = 4 + 90.25 Reorder the terms: 90.25 + -19y + y2 = 4 + 90.25 Combine like terms: 4 + 90.25 = 94.25 90.25 + -19y + y2 = 94.25 Factor a perfect square on the left side: (y + -9.5)(y + -9.5) = 94.25 Calculate the square root of the right side: 9.708243919 Break this problem into two subproblems by setting (y + -9.5) equal to 9.708243919 and -9.708243919.Subproblem 1
y + -9.5 = 9.708243919 Simplifying y + -9.5 = 9.708243919 Reorder the terms: -9.5 + y = 9.708243919 Solving -9.5 + y = 9.708243919 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + y = 9.708243919 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + y = 9.708243919 + 9.5 y = 9.708243919 + 9.5 Combine like terms: 9.708243919 + 9.5 = 19.208243919 y = 19.208243919 Simplifying y = 19.208243919Subproblem 2
y + -9.5 = -9.708243919 Simplifying y + -9.5 = -9.708243919 Reorder the terms: -9.5 + y = -9.708243919 Solving -9.5 + y = -9.708243919 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + y = -9.708243919 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + y = -9.708243919 + 9.5 y = -9.708243919 + 9.5 Combine like terms: -9.708243919 + 9.5 = -0.208243919 y = -0.208243919 Simplifying y = -0.208243919Solution
The solution to the problem is based on the solutions from the subproblems. y = {19.208243919, -0.208243919}
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