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Simplifying 3x2 + -24x + -160 = 0 Reorder the terms: -160 + -24x + 3x2 = 0 Solving -160 + -24x + 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'. -53.33333333 + -8x + x2 = 0 Move the constant term to the right: Add '53.33333333' to each side of the equation. -53.33333333 + -8x + 53.33333333 + x2 = 0 + 53.33333333 Reorder the terms: -53.33333333 + 53.33333333 + -8x + x2 = 0 + 53.33333333 Combine like terms: -53.33333333 + 53.33333333 = 0.00000000 0.00000000 + -8x + x2 = 0 + 53.33333333 -8x + x2 = 0 + 53.33333333 Combine like terms: 0 + 53.33333333 = 53.33333333 -8x + x2 = 53.33333333 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 53.33333333 + 16 Reorder the terms: 16 + -8x + x2 = 53.33333333 + 16 Combine like terms: 53.33333333 + 16 = 69.33333333 16 + -8x + x2 = 69.33333333 Factor a perfect square on the left side: (x + -4)(x + -4) = 69.33333333 Calculate the square root of the right side: 8.326663998 Break this problem into two subproblems by setting (x + -4) equal to 8.326663998 and -8.326663998.Subproblem 1
x + -4 = 8.326663998 Simplifying x + -4 = 8.326663998 Reorder the terms: -4 + x = 8.326663998 Solving -4 + x = 8.326663998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 8.326663998 + 4 Combine like terms: -4 + 4 = 0 0 + x = 8.326663998 + 4 x = 8.326663998 + 4 Combine like terms: 8.326663998 + 4 = 12.326663998 x = 12.326663998 Simplifying x = 12.326663998Subproblem 2
x + -4 = -8.326663998 Simplifying x + -4 = -8.326663998 Reorder the terms: -4 + x = -8.326663998 Solving -4 + x = -8.326663998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -8.326663998 + 4 Combine like terms: -4 + 4 = 0 0 + x = -8.326663998 + 4 x = -8.326663998 + 4 Combine like terms: -8.326663998 + 4 = -4.326663998 x = -4.326663998 Simplifying x = -4.326663998Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.326663998, -4.326663998}
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