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Simplifying 2y2 = 3y + 4 Reorder the terms: 2y2 = 4 + 3y Solving 2y2 = 4 + 3y Solving for variable 'y'. Reorder the terms: -4 + -3y + 2y2 = 4 + 3y + -4 + -3y Reorder the terms: -4 + -3y + 2y2 = 4 + -4 + 3y + -3y Combine like terms: 4 + -4 = 0 -4 + -3y + 2y2 = 0 + 3y + -3y -4 + -3y + 2y2 = 3y + -3y Combine like terms: 3y + -3y = 0 -4 + -3y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2 + -1.5y + y2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -1.5y + 2 + y2 = 0 + 2 Reorder the terms: -2 + 2 + -1.5y + y2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1.5y + y2 = 0 + 2 -1.5y + y2 = 0 + 2 Combine like terms: 0 + 2 = 2 -1.5y + y2 = 2 The y term is -1.5y. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5y + 0.5625 + y2 = 2 + 0.5625 Reorder the terms: 0.5625 + -1.5y + y2 = 2 + 0.5625 Combine like terms: 2 + 0.5625 = 2.5625 0.5625 + -1.5y + y2 = 2.5625 Factor a perfect square on the left side: (y + -0.75)(y + -0.75) = 2.5625 Calculate the square root of the right side: 1.600781059 Break this problem into two subproblems by setting (y + -0.75) equal to 1.600781059 and -1.600781059.Subproblem 1
y + -0.75 = 1.600781059 Simplifying y + -0.75 = 1.600781059 Reorder the terms: -0.75 + y = 1.600781059 Solving -0.75 + y = 1.600781059 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + y = 1.600781059 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + y = 1.600781059 + 0.75 y = 1.600781059 + 0.75 Combine like terms: 1.600781059 + 0.75 = 2.350781059 y = 2.350781059 Simplifying y = 2.350781059Subproblem 2
y + -0.75 = -1.600781059 Simplifying y + -0.75 = -1.600781059 Reorder the terms: -0.75 + y = -1.600781059 Solving -0.75 + y = -1.600781059 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + y = -1.600781059 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + y = -1.600781059 + 0.75 y = -1.600781059 + 0.75 Combine like terms: -1.600781059 + 0.75 = -0.850781059 y = -0.850781059 Simplifying y = -0.850781059Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.350781059, -0.850781059}
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