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Simplifying -350x2 + 700x + -3 = 0 Reorder the terms: -3 + 700x + -350x2 = 0 Solving -3 + 700x + -350x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -350 the coefficient of the squared term: Divide each side by '-350'. 0.008571428571 + -2x + x2 = 0 Move the constant term to the right: Add '-0.008571428571' to each side of the equation. 0.008571428571 + -2x + -0.008571428571 + x2 = 0 + -0.008571428571 Reorder the terms: 0.008571428571 + -0.008571428571 + -2x + x2 = 0 + -0.008571428571 Combine like terms: 0.008571428571 + -0.008571428571 = 0.000000000000 0.000000000000 + -2x + x2 = 0 + -0.008571428571 -2x + x2 = 0 + -0.008571428571 Combine like terms: 0 + -0.008571428571 = -0.008571428571 -2x + x2 = -0.008571428571 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -0.008571428571 + 1 Reorder the terms: 1 + -2x + x2 = -0.008571428571 + 1 Combine like terms: -0.008571428571 + 1 = 0.991428571429 1 + -2x + x2 = 0.991428571429 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.991428571429 Calculate the square root of the right side: 0.995705062 Break this problem into two subproblems by setting (x + -1) equal to 0.995705062 and -0.995705062.Subproblem 1
x + -1 = 0.995705062 Simplifying x + -1 = 0.995705062 Reorder the terms: -1 + x = 0.995705062 Solving -1 + x = 0.995705062 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0.995705062 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.995705062 + 1 x = 0.995705062 + 1 Combine like terms: 0.995705062 + 1 = 1.995705062 x = 1.995705062 Simplifying x = 1.995705062Subproblem 2
x + -1 = -0.995705062 Simplifying x + -1 = -0.995705062 Reorder the terms: -1 + x = -0.995705062 Solving -1 + x = -0.995705062 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -0.995705062 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.995705062 + 1 x = -0.995705062 + 1 Combine like terms: -0.995705062 + 1 = 0.004294938 x = 0.004294938 Simplifying x = 0.004294938Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.995705062, 0.004294938}
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