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Simplifying 9x2 + -140x + 245 = 0 Reorder the terms: 245 + -140x + 9x2 = 0 Solving 245 + -140x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 27.22222222 + -15.55555556x + x2 = 0 Move the constant term to the right: Add '-27.22222222' to each side of the equation. 27.22222222 + -15.55555556x + -27.22222222 + x2 = 0 + -27.22222222 Reorder the terms: 27.22222222 + -27.22222222 + -15.55555556x + x2 = 0 + -27.22222222 Combine like terms: 27.22222222 + -27.22222222 = 0.00000000 0.00000000 + -15.55555556x + x2 = 0 + -27.22222222 -15.55555556x + x2 = 0 + -27.22222222 Combine like terms: 0 + -27.22222222 = -27.22222222 -15.55555556x + x2 = -27.22222222 The x term is -15.55555556x. Take half its coefficient (-7.77777778). Square it (60.49382720) and add it to both sides. Add '60.49382720' to each side of the equation. -15.55555556x + 60.49382720 + x2 = -27.22222222 + 60.49382720 Reorder the terms: 60.49382720 + -15.55555556x + x2 = -27.22222222 + 60.49382720 Combine like terms: -27.22222222 + 60.49382720 = 33.27160498 60.49382720 + -15.55555556x + x2 = 33.27160498 Factor a perfect square on the left side: (x + -7.77777778)(x + -7.77777778) = 33.27160498 Calculate the square root of the right side: 5.768154382 Break this problem into two subproblems by setting (x + -7.77777778) equal to 5.768154382 and -5.768154382.Subproblem 1
x + -7.77777778 = 5.768154382 Simplifying x + -7.77777778 = 5.768154382 Reorder the terms: -7.77777778 + x = 5.768154382 Solving -7.77777778 + x = 5.768154382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.77777778' to each side of the equation. -7.77777778 + 7.77777778 + x = 5.768154382 + 7.77777778 Combine like terms: -7.77777778 + 7.77777778 = 0.00000000 0.00000000 + x = 5.768154382 + 7.77777778 x = 5.768154382 + 7.77777778 Combine like terms: 5.768154382 + 7.77777778 = 13.545932162 x = 13.545932162 Simplifying x = 13.545932162Subproblem 2
x + -7.77777778 = -5.768154382 Simplifying x + -7.77777778 = -5.768154382 Reorder the terms: -7.77777778 + x = -5.768154382 Solving -7.77777778 + x = -5.768154382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.77777778' to each side of the equation. -7.77777778 + 7.77777778 + x = -5.768154382 + 7.77777778 Combine like terms: -7.77777778 + 7.77777778 = 0.00000000 0.00000000 + x = -5.768154382 + 7.77777778 x = -5.768154382 + 7.77777778 Combine like terms: -5.768154382 + 7.77777778 = 2.009623398 x = 2.009623398 Simplifying x = 2.009623398Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.545932162, 2.009623398}
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