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Simplifying 20 = -16t2 + 32t + 0 Reorder the terms: 20 = 0 + 32t + -16t2 Remove the zero: 20 = 32t + -16t2 Solving 20 = 32t + -16t2 Solving for variable 't'. Reorder the terms: 20 + -32t + 16t2 = 32t + -32t + -16t2 + 16t2 Combine like terms: 32t + -32t = 0 20 + -32t + 16t2 = 0 + -16t2 + 16t2 20 + -32t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 20 + -32t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(5 + -8t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + -8t + 4t2)' equal to zero and attempt to solve: Simplifying 5 + -8t + 4t2 = 0 Solving 5 + -8t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + -2t + t2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -2t + -1.25 + t2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -2t + t2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -2t + t2 = 0 + -1.25 -2t + t2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -2t + t2 = -1.25 The t term is -2t. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2t + 1 + t2 = -1.25 + 1 Reorder the terms: 1 + -2t + t2 = -1.25 + 1 Combine like terms: -1.25 + 1 = -0.25 1 + -2t + t2 = -0.25 Factor a perfect square on the left side: (t + -1)(t + -1) = -0.25 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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