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Simplifying 120 = -16t2 + 4t Reorder the terms: 120 = 4t + -16t2 Solving 120 = 4t + -16t2 Solving for variable 't'. Reorder the terms: 120 + -4t + 16t2 = 4t + -4t + -16t2 + 16t2 Combine like terms: 4t + -4t = 0 120 + -4t + 16t2 = 0 + -16t2 + 16t2 120 + -4t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 120 + -4t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(30 + -1t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(30 + -1t + 4t2)' equal to zero and attempt to solve: Simplifying 30 + -1t + 4t2 = 0 Solving 30 + -1t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 7.5 + -0.25t + t2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + -0.25t + -7.5 + t2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + -0.25t + t2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + -0.25t + t2 = 0 + -7.5 -0.25t + t2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 -0.25t + t2 = -7.5 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 = -7.5 + 0.015625 Reorder the terms: 0.015625 + -0.25t + t2 = -7.5 + 0.015625 Combine like terms: -7.5 + 0.015625 = -7.484375 0.015625 + -0.25t + t2 = -7.484375 Factor a perfect square on the left side: (t + -0.125)(t + -0.125) = -7.484375 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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