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Simplifying (7y + -8y) * 2y + -4y = -2 Combine like terms: 7y + -8y = -1y (-1y) * 2y + -4y = -2 Remove parenthesis around (-1y) -1y * 2y + -4y = -2 Reorder the terms for easier multiplication: -1 * 2y * y + -4y = -2 Multiply -1 * 2 -2y * y + -4y = -2 Multiply y * y -2y2 + -4y = -2 Reorder the terms: -4y + -2y2 = -2 Solving -4y + -2y2 = -2 Solving for variable 'y'. Reorder the terms: 2 + -4y + -2y2 = -2 + 2 Combine like terms: -2 + 2 = 0 2 + -4y + -2y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -2y + -1y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -2y + -1y2)' equal to zero and attempt to solve: Simplifying 1 + -2y + -1y2 = 0 Solving 1 + -2y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1 + 2y + y2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 2y + 1 + y2 = 0 + 1 Reorder the terms: -1 + 1 + 2y + y2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2y + y2 = 0 + 1 2y + y2 = 0 + 1 Combine like terms: 0 + 1 = 1 2y + y2 = 1 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 = 1 + 1 Reorder the terms: 1 + 2y + y2 = 1 + 1 Combine like terms: 1 + 1 = 2 1 + 2y + y2 = 2 Factor a perfect square on the left side: (y + 1)(y + 1) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (y + 1) equal to 1.414213562 and -1.414213562.Subproblem 1
y + 1 = 1.414213562 Simplifying y + 1 = 1.414213562 Reorder the terms: 1 + y = 1.414213562 Solving 1 + y = 1.414213562 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 = 1.414213562 + -1 Combine like terms: 1 + -1 = 0 0 + y = 1.414213562 + -1 y = 1.414213562 + -1 Combine like terms: 1.414213562 + -1 = 0.414213562 y = 0.414213562 Simplifying y = 0.414213562Subproblem 2
y + 1 = -1.414213562 Simplifying y + 1 = -1.414213562 Reorder the terms: 1 + y = -1.414213562 Solving 1 + y = -1.414213562 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 = -1.414213562 + -1 Combine like terms: 1 + -1 = 0 0 + y = -1.414213562 + -1 y = -1.414213562 + -1 Combine like terms: -1.414213562 + -1 = -2.414213562 y = -2.414213562 Simplifying y = -2.414213562Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.414213562, -2.414213562}Solution
y = {0.414213562, -2.414213562}
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