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Simplifying 7x2 + -56x + -50 = 0 Reorder the terms: -50 + -56x + 7x2 = 0 Solving -50 + -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'. -7.142857143 + -8x + x2 = 0 Move the constant term to the right: Add '7.142857143' to each side of the equation. -7.142857143 + -8x + 7.142857143 + x2 = 0 + 7.142857143 Reorder the terms: -7.142857143 + 7.142857143 + -8x + x2 = 0 + 7.142857143 Combine like terms: -7.142857143 + 7.142857143 = 0.000000000 0.000000000 + -8x + x2 = 0 + 7.142857143 -8x + x2 = 0 + 7.142857143 Combine like terms: 0 + 7.142857143 = 7.142857143 -8x + x2 = 7.142857143 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 = 7.142857143 + 16 Reorder the terms: 16 + -8x + x2 = 7.142857143 + 16 Combine like terms: 7.142857143 + 16 = 23.142857143 16 + -8x + x2 = 23.142857143 Factor a perfect square on the left side: (x + -4)(x + -4) = 23.142857143 Calculate the square root of the right side: 4.810702354 Break this problem into two subproblems by setting (x + -4) equal to 4.810702354 and -4.810702354.Subproblem 1
x + -4 = 4.810702354 Simplifying x + -4 = 4.810702354 Reorder the terms: -4 + x = 4.810702354 Solving -4 + x = 4.810702354 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 = 4.810702354 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.810702354 + 4 x = 4.810702354 + 4 Combine like terms: 4.810702354 + 4 = 8.810702354 x = 8.810702354 Simplifying x = 8.810702354Subproblem 2
x + -4 = -4.810702354 Simplifying x + -4 = -4.810702354 Reorder the terms: -4 + x = -4.810702354 Solving -4 + x = -4.810702354 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 = -4.810702354 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.810702354 + 4 x = -4.810702354 + 4 Combine like terms: -4.810702354 + 4 = -0.810702354 x = -0.810702354 Simplifying x = -0.810702354Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.810702354, -0.810702354}
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