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Simplifying ((6y2 + 2y + -2) + -1(-1y2 + -10y + 2)) + -1(-4y2 + 3y + 3) = 0 Reorder the terms: ((-2 + 2y + 6y2) + -1(-1y2 + -10y + 2)) + -1(-4y2 + 3y + 3) = 0 Remove parenthesis around (-2 + 2y + 6y2) (-2 + 2y + 6y2 + -1(-1y2 + -10y + 2)) + -1(-4y2 + 3y + 3) = 0 Reorder the terms: (-2 + 2y + 6y2 + -1(2 + -10y + -1y2)) + -1(-4y2 + 3y + 3) = 0 (-2 + 2y + 6y2 + (2 * -1 + -10y * -1 + -1y2 * -1)) + -1(-4y2 + 3y + 3) = 0 (-2 + 2y + 6y2 + (-2 + 10y + 1y2)) + -1(-4y2 + 3y + 3) = 0 Reorder the terms: (-2 + -2 + 2y + 10y + 6y2 + 1y2) + -1(-4y2 + 3y + 3) = 0 Combine like terms: -2 + -2 = -4 (-4 + 2y + 10y + 6y2 + 1y2) + -1(-4y2 + 3y + 3) = 0 Combine like terms: 2y + 10y = 12y (-4 + 12y + 6y2 + 1y2) + -1(-4y2 + 3y + 3) = 0 Combine like terms: 6y2 + 1y2 = 7y2 (-4 + 12y + 7y2) + -1(-4y2 + 3y + 3) = 0 Remove parenthesis around (-4 + 12y + 7y2) -4 + 12y + 7y2 + -1(-4y2 + 3y + 3) = 0 Reorder the terms: -4 + 12y + 7y2 + -1(3 + 3y + -4y2) = 0 -4 + 12y + 7y2 + (3 * -1 + 3y * -1 + -4y2 * -1) = 0 -4 + 12y + 7y2 + (-3 + -3y + 4y2) = 0 Reorder the terms: -4 + -3 + 12y + -3y + 7y2 + 4y2 = 0 Combine like terms: -4 + -3 = -7 -7 + 12y + -3y + 7y2 + 4y2 = 0 Combine like terms: 12y + -3y = 9y -7 + 9y + 7y2 + 4y2 = 0 Combine like terms: 7y2 + 4y2 = 11y2 -7 + 9y + 11y2 = 0 Solving -7 + 9y + 11y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.6363636364 + 0.8181818182y + y2 = 0 Move the constant term to the right: Add '0.6363636364' to each side of the equation. -0.6363636364 + 0.8181818182y + 0.6363636364 + y2 = 0 + 0.6363636364 Reorder the terms: -0.6363636364 + 0.6363636364 + 0.8181818182y + y2 = 0 + 0.6363636364 Combine like terms: -0.6363636364 + 0.6363636364 = 0.0000000000 0.0000000000 + 0.8181818182y + y2 = 0 + 0.6363636364 0.8181818182y + y2 = 0 + 0.6363636364 Combine like terms: 0 + 0.6363636364 = 0.6363636364 0.8181818182y + y2 = 0.6363636364 The y term is 0.8181818182y. Take half its coefficient (0.4090909091). Square it (0.1673553719) and add it to both sides. Add '0.1673553719' to each side of the equation. 0.8181818182y + 0.1673553719 + y2 = 0.6363636364 + 0.1673553719 Reorder the terms: 0.1673553719 + 0.8181818182y + y2 = 0.6363636364 + 0.1673553719 Combine like terms: 0.6363636364 + 0.1673553719 = 0.8037190083 0.1673553719 + 0.8181818182y + y2 = 0.8037190083 Factor a perfect square on the left side: (y + 0.4090909091)(y + 0.4090909091) = 0.8037190083 Calculate the square root of the right side: 0.896503769 Break this problem into two subproblems by setting (y + 0.4090909091) equal to 0.896503769 and -0.896503769.Subproblem 1
y + 0.4090909091 = 0.896503769 Simplifying y + 0.4090909091 = 0.896503769 Reorder the terms: 0.4090909091 + y = 0.896503769 Solving 0.4090909091 + y = 0.896503769 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.4090909091' to each side of the equation. 0.4090909091 + -0.4090909091 + y = 0.896503769 + -0.4090909091 Combine like terms: 0.4090909091 + -0.4090909091 = 0.0000000000 0.0000000000 + y = 0.896503769 + -0.4090909091 y = 0.896503769 + -0.4090909091 Combine like terms: 0.896503769 + -0.4090909091 = 0.4874128599 y = 0.4874128599 Simplifying y = 0.4874128599Subproblem 2
y + 0.4090909091 = -0.896503769 Simplifying y + 0.4090909091 = -0.896503769 Reorder the terms: 0.4090909091 + y = -0.896503769 Solving 0.4090909091 + y = -0.896503769 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.4090909091' to each side of the equation. 0.4090909091 + -0.4090909091 + y = -0.896503769 + -0.4090909091 Combine like terms: 0.4090909091 + -0.4090909091 = 0.0000000000 0.0000000000 + y = -0.896503769 + -0.4090909091 y = -0.896503769 + -0.4090909091 Combine like terms: -0.896503769 + -0.4090909091 = -1.3055946781 y = -1.3055946781 Simplifying y = -1.3055946781Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.4874128599, -1.3055946781}
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