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Simplifying 6.28x2 + 540x + -4173 = 0 Reorder the terms: -4173 + 540x + 6.28x2 = 0 Solving -4173 + 540x + 6.28x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6.28 the coefficient of the squared term: Divide each side by '6.28'. -664.4904459 + 85.98726115x + x2 = 0 Move the constant term to the right: Add '664.4904459' to each side of the equation. -664.4904459 + 85.98726115x + 664.4904459 + x2 = 0 + 664.4904459 Reorder the terms: -664.4904459 + 664.4904459 + 85.98726115x + x2 = 0 + 664.4904459 Combine like terms: -664.4904459 + 664.4904459 = 0.0000000 0.0000000 + 85.98726115x + x2 = 0 + 664.4904459 85.98726115x + x2 = 0 + 664.4904459 Combine like terms: 0 + 664.4904459 = 664.4904459 85.98726115x + x2 = 664.4904459 The x term is 85.98726115x. Take half its coefficient (42.99363058). Square it (1848.452270) and add it to both sides. Add '1848.452270' to each side of the equation. 85.98726115x + 1848.452270 + x2 = 664.4904459 + 1848.452270 Reorder the terms: 1848.452270 + 85.98726115x + x2 = 664.4904459 + 1848.452270 Combine like terms: 664.4904459 + 1848.452270 = 2512.9427159 1848.452270 + 85.98726115x + x2 = 2512.9427159 Factor a perfect square on the left side: (x + 42.99363058)(x + 42.99363058) = 2512.9427159 Calculate the square root of the right side: 50.129260077 Break this problem into two subproblems by setting (x + 42.99363058) equal to 50.129260077 and -50.129260077.Subproblem 1
x + 42.99363058 = 50.129260077 Simplifying x + 42.99363058 = 50.129260077 Reorder the terms: 42.99363058 + x = 50.129260077 Solving 42.99363058 + x = 50.129260077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-42.99363058' to each side of the equation. 42.99363058 + -42.99363058 + x = 50.129260077 + -42.99363058 Combine like terms: 42.99363058 + -42.99363058 = 0.00000000 0.00000000 + x = 50.129260077 + -42.99363058 x = 50.129260077 + -42.99363058 Combine like terms: 50.129260077 + -42.99363058 = 7.135629497 x = 7.135629497 Simplifying x = 7.135629497Subproblem 2
x + 42.99363058 = -50.129260077 Simplifying x + 42.99363058 = -50.129260077 Reorder the terms: 42.99363058 + x = -50.129260077 Solving 42.99363058 + x = -50.129260077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-42.99363058' to each side of the equation. 42.99363058 + -42.99363058 + x = -50.129260077 + -42.99363058 Combine like terms: 42.99363058 + -42.99363058 = 0.00000000 0.00000000 + x = -50.129260077 + -42.99363058 x = -50.129260077 + -42.99363058 Combine like terms: -50.129260077 + -42.99363058 = -93.122890657 x = -93.122890657 Simplifying x = -93.122890657Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.135629497, -93.122890657}
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