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Simplifying 160t2 + 144t + 160 = 0 Reorder the terms: 160 + 144t + 160t2 = 0 Solving 160 + 144t + 160t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16'. 16(10 + 9t + 10t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(10 + 9t + 10t2)' equal to zero and attempt to solve: Simplifying 10 + 9t + 10t2 = 0 Solving 10 + 9t + 10t2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 1 + 0.9t + t2 = 0.0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 0.9t + -1 + t2 = 0.0 + -1 Reorder the terms: 1 + -1 + 0.9t + t2 = 0.0 + -1 Combine like terms: 1 + -1 = 0 0 + 0.9t + t2 = 0.0 + -1 0.9t + t2 = 0.0 + -1 Combine like terms: 0.0 + -1 = -1 0.9t + t2 = -1 The t term is 0.9t. Take half its coefficient (0.45). Square it (0.2025) and add it to both sides. Add '0.2025' to each side of the equation. 0.9t + 0.2025 + t2 = -1 + 0.2025 Reorder the terms: 0.2025 + 0.9t + t2 = -1 + 0.2025 Combine like terms: -1 + 0.2025 = -0.7975 0.2025 + 0.9t + t2 = -0.7975 Factor a perfect square on the left side: (t + 0.45)(t + 0.45) = -0.7975 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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