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Simplifying 7x2 + -20x + -5 = 0 Reorder the terms: -5 + -20x + 7x2 = 0 Solving -5 + -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'. -0.7142857143 + -2.857142857x + x2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + -2.857142857x + 0.7142857143 + x2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + -2.857142857x + x2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + -2.857142857x + x2 = 0 + 0.7142857143 -2.857142857x + x2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 -2.857142857x + x2 = 0.7142857143 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 = 0.7142857143 + 2.040816328 Reorder the terms: 2.040816328 + -2.857142857x + x2 = 0.7142857143 + 2.040816328 Combine like terms: 0.7142857143 + 2.040816328 = 2.7551020423 2.040816328 + -2.857142857x + x2 = 2.7551020423 Factor a perfect square on the left side: (x + -1.428571429)(x + -1.428571429) = 2.7551020423 Calculate the square root of the right side: 1.659850006 Break this problem into two subproblems by setting (x + -1.428571429) equal to 1.659850006 and -1.659850006.Subproblem 1
x + -1.428571429 = 1.659850006 Simplifying x + -1.428571429 = 1.659850006 Reorder the terms: -1.428571429 + x = 1.659850006 Solving -1.428571429 + x = 1.659850006 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 = 1.659850006 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = 1.659850006 + 1.428571429 x = 1.659850006 + 1.428571429 Combine like terms: 1.659850006 + 1.428571429 = 3.088421435 x = 3.088421435 Simplifying x = 3.088421435Subproblem 2
x + -1.428571429 = -1.659850006 Simplifying x + -1.428571429 = -1.659850006 Reorder the terms: -1.428571429 + x = -1.659850006 Solving -1.428571429 + x = -1.659850006 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 = -1.659850006 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = -1.659850006 + 1.428571429 x = -1.659850006 + 1.428571429 Combine like terms: -1.659850006 + 1.428571429 = -0.231278577 x = -0.231278577 Simplifying x = -0.231278577Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.088421435, -0.231278577}
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