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Simplifying (7y2 + 4y + -14) + (-6y2 + -12y + 8) = 0 Reorder the terms: (-14 + 4y + 7y2) + (-6y2 + -12y + 8) = 0 Remove parenthesis around (-14 + 4y + 7y2) -14 + 4y + 7y2 + (-6y2 + -12y + 8) = 0 Reorder the terms: -14 + 4y + 7y2 + (8 + -12y + -6y2) = 0 Remove parenthesis around (8 + -12y + -6y2) -14 + 4y + 7y2 + 8 + -12y + -6y2 = 0 Reorder the terms: -14 + 8 + 4y + -12y + 7y2 + -6y2 = 0 Combine like terms: -14 + 8 = -6 -6 + 4y + -12y + 7y2 + -6y2 = 0 Combine like terms: 4y + -12y = -8y -6 + -8y + 7y2 + -6y2 = 0 Combine like terms: 7y2 + -6y2 = 1y2 -6 + -8y + 1y2 = 0 Solving -6 + -8y + 1y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -8y + 6 + y2 = 0 + 6 Reorder the terms: -6 + 6 + -8y + y2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -8y + y2 = 0 + 6 -8y + y2 = 0 + 6 Combine like terms: 0 + 6 = 6 -8y + y2 = 6 The y term is -8y. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8y + 16 + y2 = 6 + 16 Reorder the terms: 16 + -8y + y2 = 6 + 16 Combine like terms: 6 + 16 = 22 16 + -8y + y2 = 22 Factor a perfect square on the left side: (y + -4)(y + -4) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (y + -4) equal to 4.69041576 and -4.69041576.Subproblem 1
y + -4 = 4.69041576 Simplifying y + -4 = 4.69041576 Reorder the terms: -4 + y = 4.69041576 Solving -4 + y = 4.69041576 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + y = 4.69041576 + 4 Combine like terms: -4 + 4 = 0 0 + y = 4.69041576 + 4 y = 4.69041576 + 4 Combine like terms: 4.69041576 + 4 = 8.69041576 y = 8.69041576 Simplifying y = 8.69041576Subproblem 2
y + -4 = -4.69041576 Simplifying y + -4 = -4.69041576 Reorder the terms: -4 + y = -4.69041576 Solving -4 + y = -4.69041576 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + y = -4.69041576 + 4 Combine like terms: -4 + 4 = 0 0 + y = -4.69041576 + 4 y = -4.69041576 + 4 Combine like terms: -4.69041576 + 4 = -0.69041576 y = -0.69041576 Simplifying y = -0.69041576Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.69041576, -0.69041576}
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