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Simplifying 3y2 + -9y + -7 = 0 Reorder the terms: -7 + -9y + 3y2 = 0 Solving -7 + -9y + 3y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.333333333 + -3y + y2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + -3y + 2.333333333 + y2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + -3y + y2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + -3y + y2 = 0 + 2.333333333 -3y + y2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 -3y + y2 = 2.333333333 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 = 2.333333333 + 2.25 Reorder the terms: 2.25 + -3y + y2 = 2.333333333 + 2.25 Combine like terms: 2.333333333 + 2.25 = 4.583333333 2.25 + -3y + y2 = 4.583333333 Factor a perfect square on the left side: (y + -1.5)(y + -1.5) = 4.583333333 Calculate the square root of the right side: 2.140872096 Break this problem into two subproblems by setting (y + -1.5) equal to 2.140872096 and -2.140872096.Subproblem 1
y + -1.5 = 2.140872096 Simplifying y + -1.5 = 2.140872096 Reorder the terms: -1.5 + y = 2.140872096 Solving -1.5 + y = 2.140872096 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 = 2.140872096 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = 2.140872096 + 1.5 y = 2.140872096 + 1.5 Combine like terms: 2.140872096 + 1.5 = 3.640872096 y = 3.640872096 Simplifying y = 3.640872096Subproblem 2
y + -1.5 = -2.140872096 Simplifying y + -1.5 = -2.140872096 Reorder the terms: -1.5 + y = -2.140872096 Solving -1.5 + y = -2.140872096 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 = -2.140872096 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = -2.140872096 + 1.5 y = -2.140872096 + 1.5 Combine like terms: -2.140872096 + 1.5 = -0.640872096 y = -0.640872096 Simplifying y = -0.640872096Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.640872096, -0.640872096}
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