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Simplifying 7x2 + -20x + -140 = 0 Reorder the terms: -140 + -20x + 7x2 = 0 Solving -140 + -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'. -20 + -2.857142857x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -2.857142857x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -2.857142857x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -2.857142857x + x2 = 0 + 20 -2.857142857x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -2.857142857x + x2 = 20 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 = 20 + 2.040816328 Reorder the terms: 2.040816328 + -2.857142857x + x2 = 20 + 2.040816328 Combine like terms: 20 + 2.040816328 = 22.040816328 2.040816328 + -2.857142857x + x2 = 22.040816328 Factor a perfect square on the left side: (x + -1.428571429)(x + -1.428571429) = 22.040816328 Calculate the square root of the right side: 4.694764779 Break this problem into two subproblems by setting (x + -1.428571429) equal to 4.694764779 and -4.694764779.Subproblem 1
x + -1.428571429 = 4.694764779 Simplifying x + -1.428571429 = 4.694764779 Reorder the terms: -1.428571429 + x = 4.694764779 Solving -1.428571429 + x = 4.694764779 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 = 4.694764779 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = 4.694764779 + 1.428571429 x = 4.694764779 + 1.428571429 Combine like terms: 4.694764779 + 1.428571429 = 6.123336208 x = 6.123336208 Simplifying x = 6.123336208Subproblem 2
x + -1.428571429 = -4.694764779 Simplifying x + -1.428571429 = -4.694764779 Reorder the terms: -1.428571429 + x = -4.694764779 Solving -1.428571429 + x = -4.694764779 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 = -4.694764779 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = -4.694764779 + 1.428571429 x = -4.694764779 + 1.428571429 Combine like terms: -4.694764779 + 1.428571429 = -3.26619335 x = -3.26619335 Simplifying x = -3.26619335Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.123336208, -3.26619335}
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