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Simplifying 0 = 25t2 + 29t + 9 Reorder the terms: 0 = 9 + 29t + 25t2 Solving 0 = 9 + 29t + 25t2 Solving for variable 't'. Combine like terms: 0 + -9 = -9 -9 + -29t + -25t2 = 9 + 29t + 25t2 + -9 + -29t + -25t2 Reorder the terms: -9 + -29t + -25t2 = 9 + -9 + 29t + -29t + 25t2 + -25t2 Combine like terms: 9 + -9 = 0 -9 + -29t + -25t2 = 0 + 29t + -29t + 25t2 + -25t2 -9 + -29t + -25t2 = 29t + -29t + 25t2 + -25t2 Combine like terms: 29t + -29t = 0 -9 + -29t + -25t2 = 0 + 25t2 + -25t2 -9 + -29t + -25t2 = 25t2 + -25t2 Combine like terms: 25t2 + -25t2 = 0 -9 + -29t + -25t2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(9 + 29t + 25t2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(9 + 29t + 25t2)' equal to zero and attempt to solve: Simplifying 9 + 29t + 25t2 = 0 Solving 9 + 29t + 25t2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 0.36 + 1.16t + t2 = 0 Move the constant term to the right: Add '-0.36' to each side of the equation. 0.36 + 1.16t + -0.36 + t2 = 0 + -0.36 Reorder the terms: 0.36 + -0.36 + 1.16t + t2 = 0 + -0.36 Combine like terms: 0.36 + -0.36 = 0.00 0.00 + 1.16t + t2 = 0 + -0.36 1.16t + t2 = 0 + -0.36 Combine like terms: 0 + -0.36 = -0.36 1.16t + t2 = -0.36 The t term is 1.16t. Take half its coefficient (0.58). Square it (0.3364) and add it to both sides. Add '0.3364' to each side of the equation. 1.16t + 0.3364 + t2 = -0.36 + 0.3364 Reorder the terms: 0.3364 + 1.16t + t2 = -0.36 + 0.3364 Combine like terms: -0.36 + 0.3364 = -0.0236 0.3364 + 1.16t + t2 = -0.0236 Factor a perfect square on the left side: (t + 0.58)(t + 0.58) = -0.0236 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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