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Simplifying 1927x(997x + 100987) = 37 Reorder the terms: 1927x(100987 + 997x) = 37 (100987 * 1927x + 997x * 1927x) = 37 (194601949x + 1921219x2) = 37 Solving 194601949x + 1921219x2 = 37 Solving for variable 'x'. Reorder the terms: -37 + 194601949x + 1921219x2 = 37 + -37 Combine like terms: 37 + -37 = 0 -37 + 194601949x + 1921219x2 = 0 Begin completing the square. Divide all terms by 1921219 the coefficient of the squared term: Divide each side by '1921219'. -0.00001925860612 + 101.2908726x + x2 = 0 Move the constant term to the right: Add '0.00001925860612' to each side of the equation. -0.00001925860612 + 101.2908726x + 0.00001925860612 + x2 = 0 + 0.00001925860612 Reorder the terms: -0.00001925860612 + 0.00001925860612 + 101.2908726x + x2 = 0 + 0.00001925860612 Combine like terms: -0.00001925860612 + 0.00001925860612 = 0.00000000000000 0.00000000000000 + 101.2908726x + x2 = 0 + 0.00001925860612 101.2908726x + x2 = 0 + 0.00001925860612 Combine like terms: 0 + 0.00001925860612 = 0.00001925860612 101.2908726x + x2 = 0.00001925860612 The x term is 101.2908726x. Take half its coefficient (50.6454363). Square it (2564.960218) and add it to both sides. Add '2564.960218' to each side of the equation. 101.2908726x + 2564.960218 + x2 = 0.00001925860612 + 2564.960218 Reorder the terms: 2564.960218 + 101.2908726x + x2 = 0.00001925860612 + 2564.960218 Combine like terms: 0.00001925860612 + 2564.960218 = 2564.96023725860612 2564.960218 + 101.2908726x + x2 = 2564.96023725860612 Factor a perfect square on the left side: (x + 50.6454363)(x + 50.6454363) = 2564.96023725860612 Calculate the square root of the right side: 50.64543649 Break this problem into two subproblems by setting (x + 50.6454363) equal to 50.64543649 and -50.64543649.Subproblem 1
x + 50.6454363 = 50.64543649 Simplifying x + 50.6454363 = 50.64543649 Reorder the terms: 50.6454363 + x = 50.64543649 Solving 50.6454363 + x = 50.64543649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50.6454363' to each side of the equation. 50.6454363 + -50.6454363 + x = 50.64543649 + -50.6454363 Combine like terms: 50.6454363 + -50.6454363 = 0.0000000 0.0000000 + x = 50.64543649 + -50.6454363 x = 50.64543649 + -50.6454363 Combine like terms: 50.64543649 + -50.6454363 = 0.00000019 x = 0.00000019 Simplifying x = 0.00000019Subproblem 2
x + 50.6454363 = -50.64543649 Simplifying x + 50.6454363 = -50.64543649 Reorder the terms: 50.6454363 + x = -50.64543649 Solving 50.6454363 + x = -50.64543649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50.6454363' to each side of the equation. 50.6454363 + -50.6454363 + x = -50.64543649 + -50.6454363 Combine like terms: 50.6454363 + -50.6454363 = 0.0000000 0.0000000 + x = -50.64543649 + -50.6454363 x = -50.64543649 + -50.6454363 Combine like terms: -50.64543649 + -50.6454363 = -101.29087279 x = -101.29087279 Simplifying x = -101.29087279Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.00000019, -101.29087279}
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