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Simplifying 4y2 + 17y + -7 = 0 Reorder the terms: -7 + 17y + 4y2 = 0 Solving -7 + 17y + 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'. -1.75 + 4.25y + y2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + 4.25y + 1.75 + y2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + 4.25y + y2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + 4.25y + y2 = 0 + 1.75 4.25y + y2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 4.25y + y2 = 1.75 The y term is 4.25y. Take half its coefficient (2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. 4.25y + 4.515625 + y2 = 1.75 + 4.515625 Reorder the terms: 4.515625 + 4.25y + y2 = 1.75 + 4.515625 Combine like terms: 1.75 + 4.515625 = 6.265625 4.515625 + 4.25y + y2 = 6.265625 Factor a perfect square on the left side: (y + 2.125)(y + 2.125) = 6.265625 Calculate the square root of the right side: 2.503123049 Break this problem into two subproblems by setting (y + 2.125) equal to 2.503123049 and -2.503123049.Subproblem 1
y + 2.125 = 2.503123049 Simplifying y + 2.125 = 2.503123049 Reorder the terms: 2.125 + y = 2.503123049 Solving 2.125 + y = 2.503123049 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + y = 2.503123049 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + y = 2.503123049 + -2.125 y = 2.503123049 + -2.125 Combine like terms: 2.503123049 + -2.125 = 0.378123049 y = 0.378123049 Simplifying y = 0.378123049Subproblem 2
y + 2.125 = -2.503123049 Simplifying y + 2.125 = -2.503123049 Reorder the terms: 2.125 + y = -2.503123049 Solving 2.125 + y = -2.503123049 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + y = -2.503123049 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + y = -2.503123049 + -2.125 y = -2.503123049 + -2.125 Combine like terms: -2.503123049 + -2.125 = -4.628123049 y = -4.628123049 Simplifying y = -4.628123049Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.378123049, -4.628123049}
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