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Simplifying 7x2 + -56x + 3 = 0 Reorder the terms: 3 + -56x + 7x2 = 0 Solving 3 + -56x + 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'. 0.4285714286 + -8x + x2 = 0 Move the constant term to the right: Add '-0.4285714286' to each side of the equation. 0.4285714286 + -8x + -0.4285714286 + x2 = 0 + -0.4285714286 Reorder the terms: 0.4285714286 + -0.4285714286 + -8x + x2 = 0 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + -8x + x2 = 0 + -0.4285714286 -8x + x2 = 0 + -0.4285714286 Combine like terms: 0 + -0.4285714286 = -0.4285714286 -8x + x2 = -0.4285714286 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -0.4285714286 + 16 Reorder the terms: 16 + -8x + x2 = -0.4285714286 + 16 Combine like terms: -0.4285714286 + 16 = 15.5714285714 16 + -8x + x2 = 15.5714285714 Factor a perfect square on the left side: (x + -4)(x + -4) = 15.5714285714 Calculate the square root of the right side: 3.946064948 Break this problem into two subproblems by setting (x + -4) equal to 3.946064948 and -3.946064948.Subproblem 1
x + -4 = 3.946064948 Simplifying x + -4 = 3.946064948 Reorder the terms: -4 + x = 3.946064948 Solving -4 + x = 3.946064948 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 3.946064948 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.946064948 + 4 x = 3.946064948 + 4 Combine like terms: 3.946064948 + 4 = 7.946064948 x = 7.946064948 Simplifying x = 7.946064948Subproblem 2
x + -4 = -3.946064948 Simplifying x + -4 = -3.946064948 Reorder the terms: -4 + x = -3.946064948 Solving -4 + x = -3.946064948 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -3.946064948 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.946064948 + 4 x = -3.946064948 + 4 Combine like terms: -3.946064948 + 4 = 0.053935052 x = 0.053935052 Simplifying x = 0.053935052Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.946064948, 0.053935052}
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