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Simplifying 3.5x2 + -200x + 200 = 0 Reorder the terms: 200 + -200x + 3.5x2 = 0 Solving 200 + -200x + 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'. 57.14285714 + -57.14285714x + x2 = 0 Move the constant term to the right: Add '-57.14285714' to each side of the equation. 57.14285714 + -57.14285714x + -57.14285714 + x2 = 0 + -57.14285714 Reorder the terms: 57.14285714 + -57.14285714 + -57.14285714x + x2 = 0 + -57.14285714 Combine like terms: 57.14285714 + -57.14285714 = 0.00000000 0.00000000 + -57.14285714x + x2 = 0 + -57.14285714 -57.14285714x + x2 = 0 + -57.14285714 Combine like terms: 0 + -57.14285714 = -57.14285714 -57.14285714x + x2 = -57.14285714 The x term is -57.14285714x. Take half its coefficient (-28.57142857). Square it (816.3265305) and add it to both sides. Add '816.3265305' to each side of the equation. -57.14285714x + 816.3265305 + x2 = -57.14285714 + 816.3265305 Reorder the terms: 816.3265305 + -57.14285714x + x2 = -57.14285714 + 816.3265305 Combine like terms: -57.14285714 + 816.3265305 = 759.18367336 816.3265305 + -57.14285714x + x2 = 759.18367336 Factor a perfect square on the left side: (x + -28.57142857)(x + -28.57142857) = 759.18367336 Calculate the square root of the right side: 27.553287887 Break this problem into two subproblems by setting (x + -28.57142857) equal to 27.553287887 and -27.553287887.Subproblem 1
x + -28.57142857 = 27.553287887 Simplifying x + -28.57142857 = 27.553287887 Reorder the terms: -28.57142857 + x = 27.553287887 Solving -28.57142857 + x = 27.553287887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '28.57142857' to each side of the equation. -28.57142857 + 28.57142857 + x = 27.553287887 + 28.57142857 Combine like terms: -28.57142857 + 28.57142857 = 0.00000000 0.00000000 + x = 27.553287887 + 28.57142857 x = 27.553287887 + 28.57142857 Combine like terms: 27.553287887 + 28.57142857 = 56.124716457 x = 56.124716457 Simplifying x = 56.124716457Subproblem 2
x + -28.57142857 = -27.553287887 Simplifying x + -28.57142857 = -27.553287887 Reorder the terms: -28.57142857 + x = -27.553287887 Solving -28.57142857 + x = -27.553287887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '28.57142857' to each side of the equation. -28.57142857 + 28.57142857 + x = -27.553287887 + 28.57142857 Combine like terms: -28.57142857 + 28.57142857 = 0.00000000 0.00000000 + x = -27.553287887 + 28.57142857 x = -27.553287887 + 28.57142857 Combine like terms: -27.553287887 + 28.57142857 = 1.018140683 x = 1.018140683 Simplifying x = 1.018140683Solution
The solution to the problem is based on the solutions from the subproblems. x = {56.124716457, 1.018140683}
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