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Simplifying 7x2 + -20x + -108 = 0 Reorder the terms: -108 + -20x + 7x2 = 0 Solving -108 + -20x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -15.42857143 + -2.857142857x + x2 = 0 Move the constant term to the right: Add '15.42857143' to each side of the equation. -15.42857143 + -2.857142857x + 15.42857143 + x2 = 0 + 15.42857143 Reorder the terms: -15.42857143 + 15.42857143 + -2.857142857x + x2 = 0 + 15.42857143 Combine like terms: -15.42857143 + 15.42857143 = 0.00000000 0.00000000 + -2.857142857x + x2 = 0 + 15.42857143 -2.857142857x + x2 = 0 + 15.42857143 Combine like terms: 0 + 15.42857143 = 15.42857143 -2.857142857x + x2 = 15.42857143 The x term is -2.857142857x. Take half its coefficient (-1.428571429). Square it (2.040816328) and add it to both sides. Add '2.040816328' to each side of the equation. -2.857142857x + 2.040816328 + x2 = 15.42857143 + 2.040816328 Reorder the terms: 2.040816328 + -2.857142857x + x2 = 15.42857143 + 2.040816328 Combine like terms: 15.42857143 + 2.040816328 = 17.469387758 2.040816328 + -2.857142857x + x2 = 17.469387758 Factor a perfect square on the left side: (x + -1.428571429)(x + -1.428571429) = 17.469387758 Calculate the square root of the right side: 4.179639668 Break this problem into two subproblems by setting (x + -1.428571429) equal to 4.179639668 and -4.179639668.Subproblem 1
x + -1.428571429 = 4.179639668 Simplifying x + -1.428571429 = 4.179639668 Reorder the terms: -1.428571429 + x = 4.179639668 Solving -1.428571429 + x = 4.179639668 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + x = 4.179639668 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = 4.179639668 + 1.428571429 x = 4.179639668 + 1.428571429 Combine like terms: 4.179639668 + 1.428571429 = 5.608211097 x = 5.608211097 Simplifying x = 5.608211097Subproblem 2
x + -1.428571429 = -4.179639668 Simplifying x + -1.428571429 = -4.179639668 Reorder the terms: -1.428571429 + x = -4.179639668 Solving -1.428571429 + x = -4.179639668 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + x = -4.179639668 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = -4.179639668 + 1.428571429 x = -4.179639668 + 1.428571429 Combine like terms: -4.179639668 + 1.428571429 = -2.751068239 x = -2.751068239 Simplifying x = -2.751068239Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.608211097, -2.751068239}
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