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Simplifying 3y2 + -7y + 5 = -2y2 + 4y + 6 Reorder the terms: 5 + -7y + 3y2 = -2y2 + 4y + 6 Reorder the terms: 5 + -7y + 3y2 = 6 + 4y + -2y2 Solving 5 + -7y + 3y2 = 6 + 4y + -2y2 Solving for variable 'y'. Reorder the terms: 5 + -6 + -7y + -4y + 3y2 + 2y2 = 6 + 4y + -2y2 + -6 + -4y + 2y2 Combine like terms: 5 + -6 = -1 -1 + -7y + -4y + 3y2 + 2y2 = 6 + 4y + -2y2 + -6 + -4y + 2y2 Combine like terms: -7y + -4y = -11y -1 + -11y + 3y2 + 2y2 = 6 + 4y + -2y2 + -6 + -4y + 2y2 Combine like terms: 3y2 + 2y2 = 5y2 -1 + -11y + 5y2 = 6 + 4y + -2y2 + -6 + -4y + 2y2 Reorder the terms: -1 + -11y + 5y2 = 6 + -6 + 4y + -4y + -2y2 + 2y2 Combine like terms: 6 + -6 = 0 -1 + -11y + 5y2 = 0 + 4y + -4y + -2y2 + 2y2 -1 + -11y + 5y2 = 4y + -4y + -2y2 + 2y2 Combine like terms: 4y + -4y = 0 -1 + -11y + 5y2 = 0 + -2y2 + 2y2 -1 + -11y + 5y2 = -2y2 + 2y2 Combine like terms: -2y2 + 2y2 = 0 -1 + -11y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + -2.2y + y2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -2.2y + 0.2 + y2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -2.2y + y2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -2.2y + y2 = 0 + 0.2 -2.2y + y2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -2.2y + y2 = 0.2 The y term is -2.2y. Take half its coefficient (-1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. -2.2y + 1.21 + y2 = 0.2 + 1.21 Reorder the terms: 1.21 + -2.2y + y2 = 0.2 + 1.21 Combine like terms: 0.2 + 1.21 = 1.41 1.21 + -2.2y + y2 = 1.41 Factor a perfect square on the left side: (y + -1.1)(y + -1.1) = 1.41 Calculate the square root of the right side: 1.187434209 Break this problem into two subproblems by setting (y + -1.1) equal to 1.187434209 and -1.187434209.Subproblem 1
y + -1.1 = 1.187434209 Simplifying y + -1.1 = 1.187434209 Reorder the terms: -1.1 + y = 1.187434209 Solving -1.1 + y = 1.187434209 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + y = 1.187434209 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + y = 1.187434209 + 1.1 y = 1.187434209 + 1.1 Combine like terms: 1.187434209 + 1.1 = 2.287434209 y = 2.287434209 Simplifying y = 2.287434209Subproblem 2
y + -1.1 = -1.187434209 Simplifying y + -1.1 = -1.187434209 Reorder the terms: -1.1 + y = -1.187434209 Solving -1.1 + y = -1.187434209 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + y = -1.187434209 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + y = -1.187434209 + 1.1 y = -1.187434209 + 1.1 Combine like terms: -1.187434209 + 1.1 = -0.087434209 y = -0.087434209 Simplifying y = -0.087434209Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.287434209, -0.087434209}
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