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Simplifying X(7X + -57) = 108 Reorder the terms: X(-57 + 7X) = 108 (-57 * X + 7X * X) = 108 (-57X + 7X2) = 108 Solving -57X + 7X2 = 108 Solving for variable 'X'. Reorder the terms: -108 + -57X + 7X2 = 108 + -108 Combine like terms: 108 + -108 = 0 -108 + -57X + 7X2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -15.42857143 + -8.142857143X + X2 = 0 Move the constant term to the right: Add '15.42857143' to each side of the equation. -15.42857143 + -8.142857143X + 15.42857143 + X2 = 0 + 15.42857143 Reorder the terms: -15.42857143 + 15.42857143 + -8.142857143X + X2 = 0 + 15.42857143 Combine like terms: -15.42857143 + 15.42857143 = 0.00000000 0.00000000 + -8.142857143X + X2 = 0 + 15.42857143 -8.142857143X + X2 = 0 + 15.42857143 Combine like terms: 0 + 15.42857143 = 15.42857143 -8.142857143X + X2 = 15.42857143 The X term is -8.142857143X. Take half its coefficient (-4.071428572). Square it (16.57653062) and add it to both sides. Add '16.57653062' to each side of the equation. -8.142857143X + 16.57653062 + X2 = 15.42857143 + 16.57653062 Reorder the terms: 16.57653062 + -8.142857143X + X2 = 15.42857143 + 16.57653062 Combine like terms: 15.42857143 + 16.57653062 = 32.00510205 16.57653062 + -8.142857143X + X2 = 32.00510205 Factor a perfect square on the left side: (X + -4.071428572)(X + -4.071428572) = 32.00510205 Calculate the square root of the right side: 5.657305193 Break this problem into two subproblems by setting (X + -4.071428572) equal to 5.657305193 and -5.657305193.Subproblem 1
X + -4.071428572 = 5.657305193 Simplifying X + -4.071428572 = 5.657305193 Reorder the terms: -4.071428572 + X = 5.657305193 Solving -4.071428572 + X = 5.657305193 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '4.071428572' to each side of the equation. -4.071428572 + 4.071428572 + X = 5.657305193 + 4.071428572 Combine like terms: -4.071428572 + 4.071428572 = 0.000000000 0.000000000 + X = 5.657305193 + 4.071428572 X = 5.657305193 + 4.071428572 Combine like terms: 5.657305193 + 4.071428572 = 9.728733765 X = 9.728733765 Simplifying X = 9.728733765Subproblem 2
X + -4.071428572 = -5.657305193 Simplifying X + -4.071428572 = -5.657305193 Reorder the terms: -4.071428572 + X = -5.657305193 Solving -4.071428572 + X = -5.657305193 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '4.071428572' to each side of the equation. -4.071428572 + 4.071428572 + X = -5.657305193 + 4.071428572 Combine like terms: -4.071428572 + 4.071428572 = 0.000000000 0.000000000 + X = -5.657305193 + 4.071428572 X = -5.657305193 + 4.071428572 Combine like terms: -5.657305193 + 4.071428572 = -1.585876621 X = -1.585876621 Simplifying X = -1.585876621Solution
The solution to the problem is based on the solutions from the subproblems. X = {9.728733765, -1.585876621}
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