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Simplifying -1y2 + 3y + 12 = 0 Reorder the terms: 12 + 3y + -1y2 = 0 Solving 12 + 3y + -1y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -12 + -3y + y2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -3y + 12 + y2 = 0 + 12 Reorder the terms: -12 + 12 + -3y + y2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -3y + y2 = 0 + 12 -3y + y2 = 0 + 12 Combine like terms: 0 + 12 = 12 -3y + y2 = 12 The y term is -3y. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3y + 2.25 + y2 = 12 + 2.25 Reorder the terms: 2.25 + -3y + y2 = 12 + 2.25 Combine like terms: 12 + 2.25 = 14.25 2.25 + -3y + y2 = 14.25 Factor a perfect square on the left side: (y + -1.5)(y + -1.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (y + -1.5) equal to 3.774917218 and -3.774917218.Subproblem 1
y + -1.5 = 3.774917218 Simplifying y + -1.5 = 3.774917218 Reorder the terms: -1.5 + y = 3.774917218 Solving -1.5 + y = 3.774917218 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = 3.774917218 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = 3.774917218 + 1.5 y = 3.774917218 + 1.5 Combine like terms: 3.774917218 + 1.5 = 5.274917218 y = 5.274917218 Simplifying y = 5.274917218Subproblem 2
y + -1.5 = -3.774917218 Simplifying y + -1.5 = -3.774917218 Reorder the terms: -1.5 + y = -3.774917218 Solving -1.5 + y = -3.774917218 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = -3.774917218 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = -3.774917218 + 1.5 y = -3.774917218 + 1.5 Combine like terms: -3.774917218 + 1.5 = -2.274917218 y = -2.274917218 Simplifying y = -2.274917218Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.274917218, -2.274917218}
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