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Simplifying 562.5 = 5y3 + 1.5y6 Solving 562.5 = 5y3 + 1.5y6 Solving for variable 'y'. Reorder the terms: 562.5 + -5y3 + -1.5y6 = 5y3 + -5y3 + 1.5y6 + -1.5y6 Combine like terms: 5y3 + -5y3 = 0 562.5 + -5y3 + -1.5y6 = 0 + 1.5y6 + -1.5y6 562.5 + -5y3 + -1.5y6 = 1.5y6 + -1.5y6 Combine like terms: 1.5y6 + -1.5y6 = 0.0 562.5 + -5y3 + -1.5y6 = 0.0 Begin completing the square. Divide all terms by -1.5 the coefficient of the squared term: Divide each side by '-1.5'. -375 + 3.333333333y3 + y6 = 0 Move the constant term to the right: Add '375' to each side of the equation. -375 + 3.333333333y3 + 375 + y6 = 0 + 375 Reorder the terms: -375 + 375 + 3.333333333y3 + y6 = 0 + 375 Combine like terms: -375 + 375 = 0 0 + 3.333333333y3 + y6 = 0 + 375 3.333333333y3 + y6 = 0 + 375 Combine like terms: 0 + 375 = 375 3.333333333y3 + y6 = 375 The y term is 3.333333333y3. Take half its coefficient (1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. 3.333333333y3 + 2.777777779 + y6 = 375 + 2.777777779 Reorder the terms: 2.777777779 + 3.333333333y3 + y6 = 375 + 2.777777779 Combine like terms: 375 + 2.777777779 = 377.777777779 2.777777779 + 3.333333333y3 + y6 = 377.777777779 Factor a perfect square on the left side: (y3 + 1.666666667)(y3 + 1.666666667) = 377.777777779 Calculate the square root of the right side: 19.436506316 Break this problem into two subproblems by setting (y3 + 1.666666667) equal to 19.436506316 and -19.436506316.Subproblem 1
y3 + 1.666666667 = 19.436506316 Simplifying y3 + 1.666666667 = 19.436506316 Reorder the terms: 1.666666667 + y3 = 19.436506316 Solving 1.666666667 + y3 = 19.436506316 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + y3 = 19.436506316 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + y3 = 19.436506316 + -1.666666667 y3 = 19.436506316 + -1.666666667 Combine like terms: 19.436506316 + -1.666666667 = 17.769839649 y3 = 17.769839649 Simplifying y3 = 17.769839649 Reorder the terms: -17.769839649 + y3 = 17.769839649 + -17.769839649 Combine like terms: 17.769839649 + -17.769839649 = 0.000000000 -17.769839649 + y3 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
y3 + 1.666666667 = -19.436506316 Simplifying y3 + 1.666666667 = -19.436506316 Reorder the terms: 1.666666667 + y3 = -19.436506316 Solving 1.666666667 + y3 = -19.436506316 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + y3 = -19.436506316 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + y3 = -19.436506316 + -1.666666667 y3 = -19.436506316 + -1.666666667 Combine like terms: -19.436506316 + -1.666666667 = -21.103172983 y3 = -21.103172983 Simplifying y3 = -21.103172983 Reorder the terms: 21.103172983 + y3 = -21.103172983 + 21.103172983 Combine like terms: -21.103172983 + 21.103172983 = 0.000000000 21.103172983 + y3 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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