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Simplifying -3.5x2 + 364x + -965 = 0 Reorder the terms: -965 + 364x + -3.5x2 = 0 Solving -965 + 364x + -3.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -3.5 the coefficient of the squared term: Divide each side by '-3.5'. 275.7142857 + -104x + x2 = 0 Move the constant term to the right: Add '-275.7142857' to each side of the equation. 275.7142857 + -104x + -275.7142857 + x2 = 0 + -275.7142857 Reorder the terms: 275.7142857 + -275.7142857 + -104x + x2 = 0 + -275.7142857 Combine like terms: 275.7142857 + -275.7142857 = 0.0000000 0.0000000 + -104x + x2 = 0 + -275.7142857 -104x + x2 = 0 + -275.7142857 Combine like terms: 0 + -275.7142857 = -275.7142857 -104x + x2 = -275.7142857 The x term is -104x. Take half its coefficient (-52). Square it (2704) and add it to both sides. Add '2704' to each side of the equation. -104x + 2704 + x2 = -275.7142857 + 2704 Reorder the terms: 2704 + -104x + x2 = -275.7142857 + 2704 Combine like terms: -275.7142857 + 2704 = 2428.2857143 2704 + -104x + x2 = 2428.2857143 Factor a perfect square on the left side: (x + -52)(x + -52) = 2428.2857143 Calculate the square root of the right side: 49.27763909 Break this problem into two subproblems by setting (x + -52) equal to 49.27763909 and -49.27763909.Subproblem 1
x + -52 = 49.27763909 Simplifying x + -52 = 49.27763909 Reorder the terms: -52 + x = 49.27763909 Solving -52 + x = 49.27763909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '52' to each side of the equation. -52 + 52 + x = 49.27763909 + 52 Combine like terms: -52 + 52 = 0 0 + x = 49.27763909 + 52 x = 49.27763909 + 52 Combine like terms: 49.27763909 + 52 = 101.27763909 x = 101.27763909 Simplifying x = 101.27763909Subproblem 2
x + -52 = -49.27763909 Simplifying x + -52 = -49.27763909 Reorder the terms: -52 + x = -49.27763909 Solving -52 + x = -49.27763909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '52' to each side of the equation. -52 + 52 + x = -49.27763909 + 52 Combine like terms: -52 + 52 = 0 0 + x = -49.27763909 + 52 x = -49.27763909 + 52 Combine like terms: -49.27763909 + 52 = 2.72236091 x = 2.72236091 Simplifying x = 2.72236091Solution
The solution to the problem is based on the solutions from the subproblems. x = {101.27763909, 2.72236091}
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