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Simplifying 3x2 + -96x + 182 = 0 Reorder the terms: 182 + -96x + 3x2 = 0 Solving 182 + -96x + 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'. 60.66666667 + -32x + x2 = 0 Move the constant term to the right: Add '-60.66666667' to each side of the equation. 60.66666667 + -32x + -60.66666667 + x2 = 0 + -60.66666667 Reorder the terms: 60.66666667 + -60.66666667 + -32x + x2 = 0 + -60.66666667 Combine like terms: 60.66666667 + -60.66666667 = 0.00000000 0.00000000 + -32x + x2 = 0 + -60.66666667 -32x + x2 = 0 + -60.66666667 Combine like terms: 0 + -60.66666667 = -60.66666667 -32x + x2 = -60.66666667 The x term is -32x. Take half its coefficient (-16). Square it (256) and add it to both sides. Add '256' to each side of the equation. -32x + 256 + x2 = -60.66666667 + 256 Reorder the terms: 256 + -32x + x2 = -60.66666667 + 256 Combine like terms: -60.66666667 + 256 = 195.33333333 256 + -32x + x2 = 195.33333333 Factor a perfect square on the left side: (x + -16)(x + -16) = 195.33333333 Calculate the square root of the right side: 13.976170195 Break this problem into two subproblems by setting (x + -16) equal to 13.976170195 and -13.976170195.Subproblem 1
x + -16 = 13.976170195 Simplifying x + -16 = 13.976170195 Reorder the terms: -16 + x = 13.976170195 Solving -16 + x = 13.976170195 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = 13.976170195 + 16 Combine like terms: -16 + 16 = 0 0 + x = 13.976170195 + 16 x = 13.976170195 + 16 Combine like terms: 13.976170195 + 16 = 29.976170195 x = 29.976170195 Simplifying x = 29.976170195Subproblem 2
x + -16 = -13.976170195 Simplifying x + -16 = -13.976170195 Reorder the terms: -16 + x = -13.976170195 Solving -16 + x = -13.976170195 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = -13.976170195 + 16 Combine like terms: -16 + 16 = 0 0 + x = -13.976170195 + 16 x = -13.976170195 + 16 Combine like terms: -13.976170195 + 16 = 2.023829805 x = 2.023829805 Simplifying x = 2.023829805Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.976170195, 2.023829805}
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