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Simplifying 2y * 2y + -7y + -22 = 0 Reorder the terms for easier multiplication: 2 * 2y * y + -7y + -22 = 0 Multiply 2 * 2 4y * y + -7y + -22 = 0 Multiply y * y 4y2 + -7y + -22 = 0 Reorder the terms: -22 + -7y + 4y2 = 0 Solving -22 + -7y + 4y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5.5 + -1.75y + y2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + -1.75y + 5.5 + y2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + -1.75y + y2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + -1.75y + y2 = 0 + 5.5 -1.75y + y2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 -1.75y + y2 = 5.5 The y term is -1.75y. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75y + 0.765625 + y2 = 5.5 + 0.765625 Reorder the terms: 0.765625 + -1.75y + y2 = 5.5 + 0.765625 Combine like terms: 5.5 + 0.765625 = 6.265625 0.765625 + -1.75y + y2 = 6.265625 Factor a perfect square on the left side: (y + -0.875)(y + -0.875) = 6.265625 Calculate the square root of the right side: 2.503123049 Break this problem into two subproblems by setting (y + -0.875) equal to 2.503123049 and -2.503123049.Subproblem 1
y + -0.875 = 2.503123049 Simplifying y + -0.875 = 2.503123049 Reorder the terms: -0.875 + y = 2.503123049 Solving -0.875 + y = 2.503123049 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + y = 2.503123049 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + y = 2.503123049 + 0.875 y = 2.503123049 + 0.875 Combine like terms: 2.503123049 + 0.875 = 3.378123049 y = 3.378123049 Simplifying y = 3.378123049Subproblem 2
y + -0.875 = -2.503123049 Simplifying y + -0.875 = -2.503123049 Reorder the terms: -0.875 + y = -2.503123049 Solving -0.875 + y = -2.503123049 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + y = -2.503123049 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + y = -2.503123049 + 0.875 y = -2.503123049 + 0.875 Combine like terms: -2.503123049 + 0.875 = -1.628123049 y = -1.628123049 Simplifying y = -1.628123049Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.378123049, -1.628123049}
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