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Simplifying 6y2 + -8y + 12 + -11y2 + -8y + 6 = 0 Reorder the terms: 12 + 6 + -8y + -8y + 6y2 + -11y2 = 0 Combine like terms: 12 + 6 = 18 18 + -8y + -8y + 6y2 + -11y2 = 0 Combine like terms: -8y + -8y = -16y 18 + -16y + 6y2 + -11y2 = 0 Combine like terms: 6y2 + -11y2 = -5y2 18 + -16y + -5y2 = 0 Solving 18 + -16y + -5y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -3.6 + 3.2y + y2 = 0 Move the constant term to the right: Add '3.6' to each side of the equation. -3.6 + 3.2y + 3.6 + y2 = 0 + 3.6 Reorder the terms: -3.6 + 3.6 + 3.2y + y2 = 0 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + 3.2y + y2 = 0 + 3.6 3.2y + y2 = 0 + 3.6 Combine like terms: 0 + 3.6 = 3.6 3.2y + y2 = 3.6 The y term is 3.2y. Take half its coefficient (1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. 3.2y + 2.56 + y2 = 3.6 + 2.56 Reorder the terms: 2.56 + 3.2y + y2 = 3.6 + 2.56 Combine like terms: 3.6 + 2.56 = 6.16 2.56 + 3.2y + y2 = 6.16 Factor a perfect square on the left side: (y + 1.6)(y + 1.6) = 6.16 Calculate the square root of the right side: 2.481934729 Break this problem into two subproblems by setting (y + 1.6) equal to 2.481934729 and -2.481934729.Subproblem 1
y + 1.6 = 2.481934729 Simplifying y + 1.6 = 2.481934729 Reorder the terms: 1.6 + y = 2.481934729 Solving 1.6 + y = 2.481934729 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + y = 2.481934729 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + y = 2.481934729 + -1.6 y = 2.481934729 + -1.6 Combine like terms: 2.481934729 + -1.6 = 0.881934729 y = 0.881934729 Simplifying y = 0.881934729Subproblem 2
y + 1.6 = -2.481934729 Simplifying y + 1.6 = -2.481934729 Reorder the terms: 1.6 + y = -2.481934729 Solving 1.6 + y = -2.481934729 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + y = -2.481934729 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + y = -2.481934729 + -1.6 y = -2.481934729 + -1.6 Combine like terms: -2.481934729 + -1.6 = -4.081934729 y = -4.081934729 Simplifying y = -4.081934729Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.881934729, -4.081934729}
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