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Simplifying 7x2 + -1 + 50x + -8 = 0 Reorder the terms: -1 + -8 + 50x + 7x2 = 0 Combine like terms: -1 + -8 = -9 -9 + 50x + 7x2 = 0 Solving -9 + 50x + 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'. -1.285714286 + 7.142857143x + x2 = 0 Move the constant term to the right: Add '1.285714286' to each side of the equation. -1.285714286 + 7.142857143x + 1.285714286 + x2 = 0 + 1.285714286 Reorder the terms: -1.285714286 + 1.285714286 + 7.142857143x + x2 = 0 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + 7.142857143x + x2 = 0 + 1.285714286 7.142857143x + x2 = 0 + 1.285714286 Combine like terms: 0 + 1.285714286 = 1.285714286 7.142857143x + x2 = 1.285714286 The x term is 7.142857143x. Take half its coefficient (3.571428572). Square it (12.75510204) and add it to both sides. Add '12.75510204' to each side of the equation. 7.142857143x + 12.75510204 + x2 = 1.285714286 + 12.75510204 Reorder the terms: 12.75510204 + 7.142857143x + x2 = 1.285714286 + 12.75510204 Combine like terms: 1.285714286 + 12.75510204 = 14.040816326 12.75510204 + 7.142857143x + x2 = 14.040816326 Factor a perfect square on the left side: (x + 3.571428572)(x + 3.571428572) = 14.040816326 Calculate the square root of the right side: 3.747107728 Break this problem into two subproblems by setting (x + 3.571428572) equal to 3.747107728 and -3.747107728.Subproblem 1
x + 3.571428572 = 3.747107728 Simplifying x + 3.571428572 = 3.747107728 Reorder the terms: 3.571428572 + x = 3.747107728 Solving 3.571428572 + x = 3.747107728 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.571428572' to each side of the equation. 3.571428572 + -3.571428572 + x = 3.747107728 + -3.571428572 Combine like terms: 3.571428572 + -3.571428572 = 0.000000000 0.000000000 + x = 3.747107728 + -3.571428572 x = 3.747107728 + -3.571428572 Combine like terms: 3.747107728 + -3.571428572 = 0.175679156 x = 0.175679156 Simplifying x = 0.175679156Subproblem 2
x + 3.571428572 = -3.747107728 Simplifying x + 3.571428572 = -3.747107728 Reorder the terms: 3.571428572 + x = -3.747107728 Solving 3.571428572 + x = -3.747107728 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.571428572' to each side of the equation. 3.571428572 + -3.571428572 + x = -3.747107728 + -3.571428572 Combine like terms: 3.571428572 + -3.571428572 = 0.000000000 0.000000000 + x = -3.747107728 + -3.571428572 x = -3.747107728 + -3.571428572 Combine like terms: -3.747107728 + -3.571428572 = -7.3185363 x = -7.3185363 Simplifying x = -7.3185363Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.175679156, -7.3185363}
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