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Simplifying 3700 = 28t2 + 194t + 9058 Reorder the terms: 3700 = 9058 + 194t + 28t2 Solving 3700 = 9058 + 194t + 28t2 Solving for variable 't'. Combine like terms: 3700 + -9058 = -5358 -5358 + -194t + -28t2 = 9058 + 194t + 28t2 + -9058 + -194t + -28t2 Reorder the terms: -5358 + -194t + -28t2 = 9058 + -9058 + 194t + -194t + 28t2 + -28t2 Combine like terms: 9058 + -9058 = 0 -5358 + -194t + -28t2 = 0 + 194t + -194t + 28t2 + -28t2 -5358 + -194t + -28t2 = 194t + -194t + 28t2 + -28t2 Combine like terms: 194t + -194t = 0 -5358 + -194t + -28t2 = 0 + 28t2 + -28t2 -5358 + -194t + -28t2 = 28t2 + -28t2 Combine like terms: 28t2 + -28t2 = 0 -5358 + -194t + -28t2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(2679 + 97t + 14t2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(2679 + 97t + 14t2)' equal to zero and attempt to solve: Simplifying 2679 + 97t + 14t2 = 0 Solving 2679 + 97t + 14t2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. 191.3571429 + 6.928571429t + t2 = 0 Move the constant term to the right: Add '-191.3571429' to each side of the equation. 191.3571429 + 6.928571429t + -191.3571429 + t2 = 0 + -191.3571429 Reorder the terms: 191.3571429 + -191.3571429 + 6.928571429t + t2 = 0 + -191.3571429 Combine like terms: 191.3571429 + -191.3571429 = 0.0000000 0.0000000 + 6.928571429t + t2 = 0 + -191.3571429 6.928571429t + t2 = 0 + -191.3571429 Combine like terms: 0 + -191.3571429 = -191.3571429 6.928571429t + t2 = -191.3571429 The t term is 6.928571429t. Take half its coefficient (3.464285715). Square it (12.00127552) and add it to both sides. Add '12.00127552' to each side of the equation. 6.928571429t + 12.00127552 + t2 = -191.3571429 + 12.00127552 Reorder the terms: 12.00127552 + 6.928571429t + t2 = -191.3571429 + 12.00127552 Combine like terms: -191.3571429 + 12.00127552 = -179.35586738 12.00127552 + 6.928571429t + t2 = -179.35586738 Factor a perfect square on the left side: (t + 3.464285715)(t + 3.464285715) = -179.35586738 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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