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Simplifying 160t2 + -40t + 30 = 0 Reorder the terms: 30 + -40t + 160t2 = 0 Solving 30 + -40t + 160t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '10'. 10(3 + -4t + 16t2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(3 + -4t + 16t2)' equal to zero and attempt to solve: Simplifying 3 + -4t + 16t2 = 0 Solving 3 + -4t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.1875 + -0.25t + t2 = 0 Move the constant term to the right: Add '-0.1875' to each side of the equation. 0.1875 + -0.25t + -0.1875 + t2 = 0 + -0.1875 Reorder the terms: 0.1875 + -0.1875 + -0.25t + t2 = 0 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + -0.25t + t2 = 0 + -0.1875 -0.25t + t2 = 0 + -0.1875 Combine like terms: 0 + -0.1875 = -0.1875 -0.25t + t2 = -0.1875 The t term is -0.25t. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25t + 0.015625 + t2 = -0.1875 + 0.015625 Reorder the terms: 0.015625 + -0.25t + t2 = -0.1875 + 0.015625 Combine like terms: -0.1875 + 0.015625 = -0.171875 0.015625 + -0.25t + t2 = -0.171875 Factor a perfect square on the left side: (t + -0.125)(t + -0.125) = -0.171875 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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