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Simplifying 7x2 + -46x + 5 = 0 Reorder the terms: 5 + -46x + 7x2 = 0 Solving 5 + -46x + 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 + -6.571428571x + x2 = 0 Move the constant term to the right: Add '-0.7142857143' to each side of the equation. 0.7142857143 + -6.571428571x + -0.7142857143 + x2 = 0 + -0.7142857143 Reorder the terms: 0.7142857143 + -0.7142857143 + -6.571428571x + x2 = 0 + -0.7142857143 Combine like terms: 0.7142857143 + -0.7142857143 = 0.0000000000 0.0000000000 + -6.571428571x + x2 = 0 + -0.7142857143 -6.571428571x + x2 = 0 + -0.7142857143 Combine like terms: 0 + -0.7142857143 = -0.7142857143 -6.571428571x + x2 = -0.7142857143 The x term is -6.571428571x. Take half its coefficient (-3.285714286). Square it (10.79591837) and add it to both sides. Add '10.79591837' to each side of the equation. -6.571428571x + 10.79591837 + x2 = -0.7142857143 + 10.79591837 Reorder the terms: 10.79591837 + -6.571428571x + x2 = -0.7142857143 + 10.79591837 Combine like terms: -0.7142857143 + 10.79591837 = 10.0816326557 10.79591837 + -6.571428571x + x2 = 10.0816326557 Factor a perfect square on the left side: (x + -3.285714286)(x + -3.285714286) = 10.0816326557 Calculate the square root of the right side: 3.175158682 Break this problem into two subproblems by setting (x + -3.285714286) equal to 3.175158682 and -3.175158682.Subproblem 1
x + -3.285714286 = 3.175158682 Simplifying x + -3.285714286 = 3.175158682 Reorder the terms: -3.285714286 + x = 3.175158682 Solving -3.285714286 + x = 3.175158682 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.285714286' to each side of the equation. -3.285714286 + 3.285714286 + x = 3.175158682 + 3.285714286 Combine like terms: -3.285714286 + 3.285714286 = 0.000000000 0.000000000 + x = 3.175158682 + 3.285714286 x = 3.175158682 + 3.285714286 Combine like terms: 3.175158682 + 3.285714286 = 6.460872968 x = 6.460872968 Simplifying x = 6.460872968Subproblem 2
x + -3.285714286 = -3.175158682 Simplifying x + -3.285714286 = -3.175158682 Reorder the terms: -3.285714286 + x = -3.175158682 Solving -3.285714286 + x = -3.175158682 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.285714286' to each side of the equation. -3.285714286 + 3.285714286 + x = -3.175158682 + 3.285714286 Combine like terms: -3.285714286 + 3.285714286 = 0.000000000 0.000000000 + x = -3.175158682 + 3.285714286 x = -3.175158682 + 3.285714286 Combine like terms: -3.175158682 + 3.285714286 = 0.110555604 x = 0.110555604 Simplifying x = 0.110555604Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.460872968, 0.110555604}
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