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Simplifying 7x2 + -48x + 7 = 0 Reorder the terms: 7 + -48x + 7x2 = 0 Solving 7 + -48x + 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'. 1 + -6.857142857x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -6.857142857x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -6.857142857x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -6.857142857x + x2 = 0 + -1 -6.857142857x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -6.857142857x + x2 = -1 The x term is -6.857142857x. Take half its coefficient (-3.428571429). Square it (11.75510204) and add it to both sides. Add '11.75510204' to each side of the equation. -6.857142857x + 11.75510204 + x2 = -1 + 11.75510204 Reorder the terms: 11.75510204 + -6.857142857x + x2 = -1 + 11.75510204 Combine like terms: -1 + 11.75510204 = 10.75510204 11.75510204 + -6.857142857x + x2 = 10.75510204 Factor a perfect square on the left side: (x + -3.428571429)(x + -3.428571429) = 10.75510204 Calculate the square root of the right side: 3.279497224 Break this problem into two subproblems by setting (x + -3.428571429) equal to 3.279497224 and -3.279497224.Subproblem 1
x + -3.428571429 = 3.279497224 Simplifying x + -3.428571429 = 3.279497224 Reorder the terms: -3.428571429 + x = 3.279497224 Solving -3.428571429 + x = 3.279497224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.428571429' to each side of the equation. -3.428571429 + 3.428571429 + x = 3.279497224 + 3.428571429 Combine like terms: -3.428571429 + 3.428571429 = 0.000000000 0.000000000 + x = 3.279497224 + 3.428571429 x = 3.279497224 + 3.428571429 Combine like terms: 3.279497224 + 3.428571429 = 6.708068653 x = 6.708068653 Simplifying x = 6.708068653Subproblem 2
x + -3.428571429 = -3.279497224 Simplifying x + -3.428571429 = -3.279497224 Reorder the terms: -3.428571429 + x = -3.279497224 Solving -3.428571429 + x = -3.279497224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.428571429' to each side of the equation. -3.428571429 + 3.428571429 + x = -3.279497224 + 3.428571429 Combine like terms: -3.428571429 + 3.428571429 = 0.000000000 0.000000000 + x = -3.279497224 + 3.428571429 x = -3.279497224 + 3.428571429 Combine like terms: -3.279497224 + 3.428571429 = 0.149074205 x = 0.149074205 Simplifying x = 0.149074205Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.708068653, 0.149074205}
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