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Simplifying 3x2 + -91x + -316 = 0 Reorder the terms: -316 + -91x + 3x2 = 0 Solving -316 + -91x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -105.3333333 + -30.33333333x + x2 = 0 Move the constant term to the right: Add '105.3333333' to each side of the equation. -105.3333333 + -30.33333333x + 105.3333333 + x2 = 0 + 105.3333333 Reorder the terms: -105.3333333 + 105.3333333 + -30.33333333x + x2 = 0 + 105.3333333 Combine like terms: -105.3333333 + 105.3333333 = 0.0000000 0.0000000 + -30.33333333x + x2 = 0 + 105.3333333 -30.33333333x + x2 = 0 + 105.3333333 Combine like terms: 0 + 105.3333333 = 105.3333333 -30.33333333x + x2 = 105.3333333 The x term is -30.33333333x. Take half its coefficient (-15.16666667). Square it (230.0277779) and add it to both sides. Add '230.0277779' to each side of the equation. -30.33333333x + 230.0277779 + x2 = 105.3333333 + 230.0277779 Reorder the terms: 230.0277779 + -30.33333333x + x2 = 105.3333333 + 230.0277779 Combine like terms: 105.3333333 + 230.0277779 = 335.3611112 230.0277779 + -30.33333333x + x2 = 335.3611112 Factor a perfect square on the left side: (x + -15.16666667)(x + -15.16666667) = 335.3611112 Calculate the square root of the right side: 18.312867367 Break this problem into two subproblems by setting (x + -15.16666667) equal to 18.312867367 and -18.312867367.Subproblem 1
x + -15.16666667 = 18.312867367 Simplifying x + -15.16666667 = 18.312867367 Reorder the terms: -15.16666667 + x = 18.312867367 Solving -15.16666667 + x = 18.312867367 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.16666667' to each side of the equation. -15.16666667 + 15.16666667 + x = 18.312867367 + 15.16666667 Combine like terms: -15.16666667 + 15.16666667 = 0.00000000 0.00000000 + x = 18.312867367 + 15.16666667 x = 18.312867367 + 15.16666667 Combine like terms: 18.312867367 + 15.16666667 = 33.479534037 x = 33.479534037 Simplifying x = 33.479534037Subproblem 2
x + -15.16666667 = -18.312867367 Simplifying x + -15.16666667 = -18.312867367 Reorder the terms: -15.16666667 + x = -18.312867367 Solving -15.16666667 + x = -18.312867367 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.16666667' to each side of the equation. -15.16666667 + 15.16666667 + x = -18.312867367 + 15.16666667 Combine like terms: -15.16666667 + 15.16666667 = 0.00000000 0.00000000 + x = -18.312867367 + 15.16666667 x = -18.312867367 + 15.16666667 Combine like terms: -18.312867367 + 15.16666667 = -3.146200697 x = -3.146200697 Simplifying x = -3.146200697Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.479534037, -3.146200697}
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