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Simplifying 6y2 + -47y + 62 = 0 Reorder the terms: 62 + -47y + 6y2 = 0 Solving 62 + -47y + 6y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 10.33333333 + -7.833333333y + y2 = 0 Move the constant term to the right: Add '-10.33333333' to each side of the equation. 10.33333333 + -7.833333333y + -10.33333333 + y2 = 0 + -10.33333333 Reorder the terms: 10.33333333 + -10.33333333 + -7.833333333y + y2 = 0 + -10.33333333 Combine like terms: 10.33333333 + -10.33333333 = 0.00000000 0.00000000 + -7.833333333y + y2 = 0 + -10.33333333 -7.833333333y + y2 = 0 + -10.33333333 Combine like terms: 0 + -10.33333333 = -10.33333333 -7.833333333y + y2 = -10.33333333 The y term is -7.833333333y. Take half its coefficient (-3.916666667). Square it (15.34027778) and add it to both sides. Add '15.34027778' to each side of the equation. -7.833333333y + 15.34027778 + y2 = -10.33333333 + 15.34027778 Reorder the terms: 15.34027778 + -7.833333333y + y2 = -10.33333333 + 15.34027778 Combine like terms: -10.33333333 + 15.34027778 = 5.00694445 15.34027778 + -7.833333333y + y2 = 5.00694445 Factor a perfect square on the left side: (y + -3.916666667)(y + -3.916666667) = 5.00694445 Calculate the square root of the right side: 2.237620265 Break this problem into two subproblems by setting (y + -3.916666667) equal to 2.237620265 and -2.237620265.Subproblem 1
y + -3.916666667 = 2.237620265 Simplifying y + -3.916666667 = 2.237620265 Reorder the terms: -3.916666667 + y = 2.237620265 Solving -3.916666667 + y = 2.237620265 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.916666667' to each side of the equation. -3.916666667 + 3.916666667 + y = 2.237620265 + 3.916666667 Combine like terms: -3.916666667 + 3.916666667 = 0.000000000 0.000000000 + y = 2.237620265 + 3.916666667 y = 2.237620265 + 3.916666667 Combine like terms: 2.237620265 + 3.916666667 = 6.154286932 y = 6.154286932 Simplifying y = 6.154286932Subproblem 2
y + -3.916666667 = -2.237620265 Simplifying y + -3.916666667 = -2.237620265 Reorder the terms: -3.916666667 + y = -2.237620265 Solving -3.916666667 + y = -2.237620265 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.916666667' to each side of the equation. -3.916666667 + 3.916666667 + y = -2.237620265 + 3.916666667 Combine like terms: -3.916666667 + 3.916666667 = 0.000000000 0.000000000 + y = -2.237620265 + 3.916666667 y = -2.237620265 + 3.916666667 Combine like terms: -2.237620265 + 3.916666667 = 1.679046402 y = 1.679046402 Simplifying y = 1.679046402Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.154286932, 1.679046402}
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