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Simplifying 6x2 + -51x + -182 = 0 Reorder the terms: -182 + -51x + 6x2 = 0 Solving -182 + -51x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -30.33333333 + -8.5x + x2 = 0 Move the constant term to the right: Add '30.33333333' to each side of the equation. -30.33333333 + -8.5x + 30.33333333 + x2 = 0 + 30.33333333 Reorder the terms: -30.33333333 + 30.33333333 + -8.5x + x2 = 0 + 30.33333333 Combine like terms: -30.33333333 + 30.33333333 = 0.00000000 0.00000000 + -8.5x + x2 = 0 + 30.33333333 -8.5x + x2 = 0 + 30.33333333 Combine like terms: 0 + 30.33333333 = 30.33333333 -8.5x + x2 = 30.33333333 The x term is -8.5x. Take half its coefficient (-4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. -8.5x + 18.0625 + x2 = 30.33333333 + 18.0625 Reorder the terms: 18.0625 + -8.5x + x2 = 30.33333333 + 18.0625 Combine like terms: 30.33333333 + 18.0625 = 48.39583333 18.0625 + -8.5x + x2 = 48.39583333 Factor a perfect square on the left side: (x + -4.25)(x + -4.25) = 48.39583333 Calculate the square root of the right side: 6.956711388 Break this problem into two subproblems by setting (x + -4.25) equal to 6.956711388 and -6.956711388.Subproblem 1
x + -4.25 = 6.956711388 Simplifying x + -4.25 = 6.956711388 Reorder the terms: -4.25 + x = 6.956711388 Solving -4.25 + x = 6.956711388 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = 6.956711388 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = 6.956711388 + 4.25 x = 6.956711388 + 4.25 Combine like terms: 6.956711388 + 4.25 = 11.206711388 x = 11.206711388 Simplifying x = 11.206711388Subproblem 2
x + -4.25 = -6.956711388 Simplifying x + -4.25 = -6.956711388 Reorder the terms: -4.25 + x = -6.956711388 Solving -4.25 + x = -6.956711388 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = -6.956711388 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = -6.956711388 + 4.25 x = -6.956711388 + 4.25 Combine like terms: -6.956711388 + 4.25 = -2.706711388 x = -2.706711388 Simplifying x = -2.706711388Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.206711388, -2.706711388}
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