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Simplifying 400 = -16t2 + 20t Reorder the terms: 400 = 20t + -16t2 Solving 400 = 20t + -16t2 Solving for variable 't'. Reorder the terms: 400 + -20t + 16t2 = 20t + -20t + -16t2 + 16t2 Combine like terms: 20t + -20t = 0 400 + -20t + 16t2 = 0 + -16t2 + 16t2 400 + -20t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 400 + -20t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(100 + -5t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(100 + -5t + 4t2)' equal to zero and attempt to solve: Simplifying 100 + -5t + 4t2 = 0 Solving 100 + -5t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 25 + -1.25t + t2 = 0 Move the constant term to the right: Add '-25' to each side of the equation. 25 + -1.25t + -25 + t2 = 0 + -25 Reorder the terms: 25 + -25 + -1.25t + t2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -1.25t + t2 = 0 + -25 -1.25t + t2 = 0 + -25 Combine like terms: 0 + -25 = -25 -1.25t + t2 = -25 The t term is -1.25t. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25t + 0.390625 + t2 = -25 + 0.390625 Reorder the terms: 0.390625 + -1.25t + t2 = -25 + 0.390625 Combine like terms: -25 + 0.390625 = -24.609375 0.390625 + -1.25t + t2 = -24.609375 Factor a perfect square on the left side: (t + -0.625)(t + -0.625) = -24.609375 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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