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Simplifying -12y + -2y2 = 84 Solving -12y + -2y2 = 84 Solving for variable 'y'. Reorder the terms: -84 + -12y + -2y2 = 84 + -84 Combine like terms: 84 + -84 = 0 -84 + -12y + -2y2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(42 + 6y + y2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(42 + 6y + y2)' equal to zero and attempt to solve: Simplifying 42 + 6y + y2 = 0 Solving 42 + 6y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-42' to each side of the equation. 42 + 6y + -42 + y2 = 0 + -42 Reorder the terms: 42 + -42 + 6y + y2 = 0 + -42 Combine like terms: 42 + -42 = 0 0 + 6y + y2 = 0 + -42 6y + y2 = 0 + -42 Combine like terms: 0 + -42 = -42 6y + y2 = -42 The y term is 6y. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6y + 9 + y2 = -42 + 9 Reorder the terms: 9 + 6y + y2 = -42 + 9 Combine like terms: -42 + 9 = -33 9 + 6y + y2 = -33 Factor a perfect square on the left side: (y + 3)(y + 3) = -33 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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