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Simplifying 0 = y2 + -12y + -80 Reorder the terms: 0 = -80 + -12y + y2 Solving 0 = -80 + -12y + y2 Solving for variable 'y'. Combine like terms: 0 + 80 = 80 80 + 12y + -1y2 = -80 + -12y + y2 + 80 + 12y + -1y2 Reorder the terms: 80 + 12y + -1y2 = -80 + 80 + -12y + 12y + y2 + -1y2 Combine like terms: -80 + 80 = 0 80 + 12y + -1y2 = 0 + -12y + 12y + y2 + -1y2 80 + 12y + -1y2 = -12y + 12y + y2 + -1y2 Combine like terms: -12y + 12y = 0 80 + 12y + -1y2 = 0 + y2 + -1y2 80 + 12y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 80 + 12y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -80 + -12y + y2 = 0 Move the constant term to the right: Add '80' to each side of the equation. -80 + -12y + 80 + y2 = 0 + 80 Reorder the terms: -80 + 80 + -12y + y2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + -12y + y2 = 0 + 80 -12y + y2 = 0 + 80 Combine like terms: 0 + 80 = 80 -12y + y2 = 80 The y term is -12y. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12y + 36 + y2 = 80 + 36 Reorder the terms: 36 + -12y + y2 = 80 + 36 Combine like terms: 80 + 36 = 116 36 + -12y + y2 = 116 Factor a perfect square on the left side: (y + -6)(y + -6) = 116 Calculate the square root of the right side: 10.770329614 Break this problem into two subproblems by setting (y + -6) equal to 10.770329614 and -10.770329614.Subproblem 1
y + -6 = 10.770329614 Simplifying y + -6 = 10.770329614 Reorder the terms: -6 + y = 10.770329614 Solving -6 + y = 10.770329614 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = 10.770329614 + 6 Combine like terms: -6 + 6 = 0 0 + y = 10.770329614 + 6 y = 10.770329614 + 6 Combine like terms: 10.770329614 + 6 = 16.770329614 y = 16.770329614 Simplifying y = 16.770329614Subproblem 2
y + -6 = -10.770329614 Simplifying y + -6 = -10.770329614 Reorder the terms: -6 + y = -10.770329614 Solving -6 + y = -10.770329614 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = -10.770329614 + 6 Combine like terms: -6 + 6 = 0 0 + y = -10.770329614 + 6 y = -10.770329614 + 6 Combine like terms: -10.770329614 + 6 = -4.770329614 y = -4.770329614 Simplifying y = -4.770329614Solution
The solution to the problem is based on the solutions from the subproblems. y = {16.770329614, -4.770329614}
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