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Simplifying -3y2 + 6y + 13 = 0 Reorder the terms: 13 + 6y + -3y2 = 0 Solving 13 + 6y + -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'. -4.333333333 + -2y + y2 = 0 Move the constant term to the right: Add '4.333333333' to each side of the equation. -4.333333333 + -2y + 4.333333333 + y2 = 0 + 4.333333333 Reorder the terms: -4.333333333 + 4.333333333 + -2y + y2 = 0 + 4.333333333 Combine like terms: -4.333333333 + 4.333333333 = 0.000000000 0.000000000 + -2y + y2 = 0 + 4.333333333 -2y + y2 = 0 + 4.333333333 Combine like terms: 0 + 4.333333333 = 4.333333333 -2y + y2 = 4.333333333 The y term is -2y. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2y + 1 + y2 = 4.333333333 + 1 Reorder the terms: 1 + -2y + y2 = 4.333333333 + 1 Combine like terms: 4.333333333 + 1 = 5.333333333 1 + -2y + y2 = 5.333333333 Factor a perfect square on the left side: (y + -1)(y + -1) = 5.333333333 Calculate the square root of the right side: 2.309401077 Break this problem into two subproblems by setting (y + -1) equal to 2.309401077 and -2.309401077.Subproblem 1
y + -1 = 2.309401077 Simplifying y + -1 = 2.309401077 Reorder the terms: -1 + y = 2.309401077 Solving -1 + y = 2.309401077 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = 2.309401077 + 1 Combine like terms: -1 + 1 = 0 0 + y = 2.309401077 + 1 y = 2.309401077 + 1 Combine like terms: 2.309401077 + 1 = 3.309401077 y = 3.309401077 Simplifying y = 3.309401077Subproblem 2
y + -1 = -2.309401077 Simplifying y + -1 = -2.309401077 Reorder the terms: -1 + y = -2.309401077 Solving -1 + y = -2.309401077 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = -2.309401077 + 1 Combine like terms: -1 + 1 = 0 0 + y = -2.309401077 + 1 y = -2.309401077 + 1 Combine like terms: -2.309401077 + 1 = -1.309401077 y = -1.309401077 Simplifying y = -1.309401077Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.309401077, -1.309401077}
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