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Simplifying 14y2 + -19y + 4 = 11y2 + 11y + -5 Reorder the terms: 4 + -19y + 14y2 = 11y2 + 11y + -5 Reorder the terms: 4 + -19y + 14y2 = -5 + 11y + 11y2 Solving 4 + -19y + 14y2 = -5 + 11y + 11y2 Solving for variable 'y'. Reorder the terms: 4 + 5 + -19y + -11y + 14y2 + -11y2 = -5 + 11y + 11y2 + 5 + -11y + -11y2 Combine like terms: 4 + 5 = 9 9 + -19y + -11y + 14y2 + -11y2 = -5 + 11y + 11y2 + 5 + -11y + -11y2 Combine like terms: -19y + -11y = -30y 9 + -30y + 14y2 + -11y2 = -5 + 11y + 11y2 + 5 + -11y + -11y2 Combine like terms: 14y2 + -11y2 = 3y2 9 + -30y + 3y2 = -5 + 11y + 11y2 + 5 + -11y + -11y2 Reorder the terms: 9 + -30y + 3y2 = -5 + 5 + 11y + -11y + 11y2 + -11y2 Combine like terms: -5 + 5 = 0 9 + -30y + 3y2 = 0 + 11y + -11y + 11y2 + -11y2 9 + -30y + 3y2 = 11y + -11y + 11y2 + -11y2 Combine like terms: 11y + -11y = 0 9 + -30y + 3y2 = 0 + 11y2 + -11y2 9 + -30y + 3y2 = 11y2 + -11y2 Combine like terms: 11y2 + -11y2 = 0 9 + -30y + 3y2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(3 + -10y + y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + -10y + y2)' equal to zero and attempt to solve: Simplifying 3 + -10y + y2 = 0 Solving 3 + -10y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -10y + -3 + y2 = 0 + -3 Reorder the terms: 3 + -3 + -10y + y2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -10y + y2 = 0 + -3 -10y + y2 = 0 + -3 Combine like terms: 0 + -3 = -3 -10y + y2 = -3 The y term is -10y. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10y + 25 + y2 = -3 + 25 Reorder the terms: 25 + -10y + y2 = -3 + 25 Combine like terms: -3 + 25 = 22 25 + -10y + y2 = 22 Factor a perfect square on the left side: (y + -5)(y + -5) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (y + -5) equal to 4.69041576 and -4.69041576.Subproblem 1
y + -5 = 4.69041576 Simplifying y + -5 = 4.69041576 Reorder the terms: -5 + y = 4.69041576 Solving -5 + y = 4.69041576 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + y = 4.69041576 + 5 Combine like terms: -5 + 5 = 0 0 + y = 4.69041576 + 5 y = 4.69041576 + 5 Combine like terms: 4.69041576 + 5 = 9.69041576 y = 9.69041576 Simplifying y = 9.69041576Subproblem 2
y + -5 = -4.69041576 Simplifying y + -5 = -4.69041576 Reorder the terms: -5 + y = -4.69041576 Solving -5 + y = -4.69041576 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + y = -4.69041576 + 5 Combine like terms: -5 + 5 = 0 0 + y = -4.69041576 + 5 y = -4.69041576 + 5 Combine like terms: -4.69041576 + 5 = 0.30958424 y = 0.30958424 Simplifying y = 0.30958424Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.69041576, 0.30958424}Solution
y = {9.69041576, 0.30958424}
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