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Simplifying 18 = y2 + 12.25y Reorder the terms: 18 = 12.25y + y2 Solving 18 = 12.25y + y2 Solving for variable 'y'. Reorder the terms: 18 + -12.25y + -1y2 = 12.25y + -12.25y + y2 + -1y2 Combine like terms: 12.25y + -12.25y = 0.00 18 + -12.25y + -1y2 = 0.00 + y2 + -1y2 18 + -12.25y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 18 + -12.25y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -18 + 12.25y + y2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + 12.25y + 18 + y2 = 0 + 18 Reorder the terms: -18 + 18 + 12.25y + y2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 12.25y + y2 = 0 + 18 12.25y + y2 = 0 + 18 Combine like terms: 0 + 18 = 18 12.25y + y2 = 18 The y term is 12.25y. Take half its coefficient (6.125). Square it (37.515625) and add it to both sides. Add '37.515625' to each side of the equation. 12.25y + 37.515625 + y2 = 18 + 37.515625 Reorder the terms: 37.515625 + 12.25y + y2 = 18 + 37.515625 Combine like terms: 18 + 37.515625 = 55.515625 37.515625 + 12.25y + y2 = 55.515625 Factor a perfect square on the left side: (y + 6.125)(y + 6.125) = 55.515625 Calculate the square root of the right side: 7.45088082 Break this problem into two subproblems by setting (y + 6.125) equal to 7.45088082 and -7.45088082.Subproblem 1
y + 6.125 = 7.45088082 Simplifying y + 6.125 = 7.45088082 Reorder the terms: 6.125 + y = 7.45088082 Solving 6.125 + y = 7.45088082 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-6.125' to each side of the equation. 6.125 + -6.125 + y = 7.45088082 + -6.125 Combine like terms: 6.125 + -6.125 = 0.000 0.000 + y = 7.45088082 + -6.125 y = 7.45088082 + -6.125 Combine like terms: 7.45088082 + -6.125 = 1.32588082 y = 1.32588082 Simplifying y = 1.32588082Subproblem 2
y + 6.125 = -7.45088082 Simplifying y + 6.125 = -7.45088082 Reorder the terms: 6.125 + y = -7.45088082 Solving 6.125 + y = -7.45088082 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-6.125' to each side of the equation. 6.125 + -6.125 + y = -7.45088082 + -6.125 Combine like terms: 6.125 + -6.125 = 0.000 0.000 + y = -7.45088082 + -6.125 y = -7.45088082 + -6.125 Combine like terms: -7.45088082 + -6.125 = -13.57588082 y = -13.57588082 Simplifying y = -13.57588082Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.32588082, -13.57588082}
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