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Simplifying 8t2 + 8t + 450 = 0 Reorder the terms: 450 + 8t + 8t2 = 0 Solving 450 + 8t + 8t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(225 + 4t + 4t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(225 + 4t + 4t2)' equal to zero and attempt to solve: Simplifying 225 + 4t + 4t2 = 0 Solving 225 + 4t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 56.25 + t + t2 = 0 Move the constant term to the right: Add '-56.25' to each side of the equation. 56.25 + t + -56.25 + t2 = 0 + -56.25 Reorder the terms: 56.25 + -56.25 + t + t2 = 0 + -56.25 Combine like terms: 56.25 + -56.25 = 0.00 0.00 + t + t2 = 0 + -56.25 t + t2 = 0 + -56.25 Combine like terms: 0 + -56.25 = -56.25 t + t2 = -56.25 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + t2 = -56.25 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + t2 = -56.25 + 0.25 Combine like terms: -56.25 + 0.25 = -56 1.25 + t2 = -56 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = -56 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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