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Simplifying 74x2 + -100000x + 654554 = 6565 Reorder the terms: 654554 + -100000x + 74x2 = 6565 Solving 654554 + -100000x + 74x2 = 6565 Solving for variable 'x'. Reorder the terms: 654554 + -6565 + -100000x + 74x2 = 6565 + -6565 Combine like terms: 654554 + -6565 = 647989 647989 + -100000x + 74x2 = 6565 + -6565 Combine like terms: 6565 + -6565 = 0 647989 + -100000x + 74x2 = 0 Begin completing the square. Divide all terms by 74 the coefficient of the squared term: Divide each side by '74'. 8756.608108 + -1351.351351x + x2 = 0 Move the constant term to the right: Add '-8756.608108' to each side of the equation. 8756.608108 + -1351.351351x + -8756.608108 + x2 = 0 + -8756.608108 Reorder the terms: 8756.608108 + -8756.608108 + -1351.351351x + x2 = 0 + -8756.608108 Combine like terms: 8756.608108 + -8756.608108 = 0.000000 0.000000 + -1351.351351x + x2 = 0 + -8756.608108 -1351.351351x + x2 = 0 + -8756.608108 Combine like terms: 0 + -8756.608108 = -8756.608108 -1351.351351x + x2 = -8756.608108 The x term is -1351.351351x. Take half its coefficient (-675.6756755). Square it (456537.6185) and add it to both sides. Add '456537.6185' to each side of the equation. -1351.351351x + 456537.6185 + x2 = -8756.608108 + 456537.6185 Reorder the terms: 456537.6185 + -1351.351351x + x2 = -8756.608108 + 456537.6185 Combine like terms: -8756.608108 + 456537.6185 = 447781.010392 456537.6185 + -1351.351351x + x2 = 447781.010392 Factor a perfect square on the left side: (x + -675.6756755)(x + -675.6756755) = 447781.010392 Calculate the square root of the right side: 669.164412078 Break this problem into two subproblems by setting (x + -675.6756755) equal to 669.164412078 and -669.164412078.Subproblem 1
x + -675.6756755 = 669.164412078 Simplifying x + -675.6756755 = 669.164412078 Reorder the terms: -675.6756755 + x = 669.164412078 Solving -675.6756755 + x = 669.164412078 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '675.6756755' to each side of the equation. -675.6756755 + 675.6756755 + x = 669.164412078 + 675.6756755 Combine like terms: -675.6756755 + 675.6756755 = 0.0000000 0.0000000 + x = 669.164412078 + 675.6756755 x = 669.164412078 + 675.6756755 Combine like terms: 669.164412078 + 675.6756755 = 1344.840087578 x = 1344.840087578 Simplifying x = 1344.840087578Subproblem 2
x + -675.6756755 = -669.164412078 Simplifying x + -675.6756755 = -669.164412078 Reorder the terms: -675.6756755 + x = -669.164412078 Solving -675.6756755 + x = -669.164412078 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '675.6756755' to each side of the equation. -675.6756755 + 675.6756755 + x = -669.164412078 + 675.6756755 Combine like terms: -675.6756755 + 675.6756755 = 0.0000000 0.0000000 + x = -669.164412078 + 675.6756755 x = -669.164412078 + 675.6756755 Combine like terms: -669.164412078 + 675.6756755 = 6.511263422 x = 6.511263422 Simplifying x = 6.511263422Solution
The solution to the problem is based on the solutions from the subproblems. x = {1344.840087578, 6.511263422}
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