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Simplifying 580 = 15y2 + 1166y Reorder the terms: 580 = 1166y + 15y2 Solving 580 = 1166y + 15y2 Solving for variable 'y'. Reorder the terms: 580 + -1166y + -15y2 = 1166y + -1166y + 15y2 + -15y2 Combine like terms: 1166y + -1166y = 0 580 + -1166y + -15y2 = 0 + 15y2 + -15y2 580 + -1166y + -15y2 = 15y2 + -15y2 Combine like terms: 15y2 + -15y2 = 0 580 + -1166y + -15y2 = 0 Begin completing the square. Divide all terms by -15 the coefficient of the squared term: Divide each side by '-15'. -38.66666667 + 77.73333333y + y2 = 0 Move the constant term to the right: Add '38.66666667' to each side of the equation. -38.66666667 + 77.73333333y + 38.66666667 + y2 = 0 + 38.66666667 Reorder the terms: -38.66666667 + 38.66666667 + 77.73333333y + y2 = 0 + 38.66666667 Combine like terms: -38.66666667 + 38.66666667 = 0.00000000 0.00000000 + 77.73333333y + y2 = 0 + 38.66666667 77.73333333y + y2 = 0 + 38.66666667 Combine like terms: 0 + 38.66666667 = 38.66666667 77.73333333y + y2 = 38.66666667 The y term is 77.73333333y. Take half its coefficient (38.86666667). Square it (1510.617778) and add it to both sides. Add '1510.617778' to each side of the equation. 77.73333333y + 1510.617778 + y2 = 38.66666667 + 1510.617778 Reorder the terms: 1510.617778 + 77.73333333y + y2 = 38.66666667 + 1510.617778 Combine like terms: 38.66666667 + 1510.617778 = 1549.28444467 1510.617778 + 77.73333333y + y2 = 1549.28444467 Factor a perfect square on the left side: (y + 38.86666667)(y + 38.86666667) = 1549.28444467 Calculate the square root of the right side: 39.360950759 Break this problem into two subproblems by setting (y + 38.86666667) equal to 39.360950759 and -39.360950759.Subproblem 1
y + 38.86666667 = 39.360950759 Simplifying y + 38.86666667 = 39.360950759 Reorder the terms: 38.86666667 + y = 39.360950759 Solving 38.86666667 + y = 39.360950759 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-38.86666667' to each side of the equation. 38.86666667 + -38.86666667 + y = 39.360950759 + -38.86666667 Combine like terms: 38.86666667 + -38.86666667 = 0.00000000 0.00000000 + y = 39.360950759 + -38.86666667 y = 39.360950759 + -38.86666667 Combine like terms: 39.360950759 + -38.86666667 = 0.494284089 y = 0.494284089 Simplifying y = 0.494284089Subproblem 2
y + 38.86666667 = -39.360950759 Simplifying y + 38.86666667 = -39.360950759 Reorder the terms: 38.86666667 + y = -39.360950759 Solving 38.86666667 + y = -39.360950759 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-38.86666667' to each side of the equation. 38.86666667 + -38.86666667 + y = -39.360950759 + -38.86666667 Combine like terms: 38.86666667 + -38.86666667 = 0.00000000 0.00000000 + y = -39.360950759 + -38.86666667 y = -39.360950759 + -38.86666667 Combine like terms: -39.360950759 + -38.86666667 = -78.227617429 y = -78.227617429 Simplifying y = -78.227617429Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.494284089, -78.227617429}
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