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Simplifying 0 = 16t2 + 65t + 160 Reorder the terms: 0 = 160 + 65t + 16t2 Solving 0 = 160 + 65t + 16t2 Solving for variable 't'. Combine like terms: 0 + -160 = -160 -160 + -65t + -16t2 = 160 + 65t + 16t2 + -160 + -65t + -16t2 Reorder the terms: -160 + -65t + -16t2 = 160 + -160 + 65t + -65t + 16t2 + -16t2 Combine like terms: 160 + -160 = 0 -160 + -65t + -16t2 = 0 + 65t + -65t + 16t2 + -16t2 -160 + -65t + -16t2 = 65t + -65t + 16t2 + -16t2 Combine like terms: 65t + -65t = 0 -160 + -65t + -16t2 = 0 + 16t2 + -16t2 -160 + -65t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -160 + -65t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(160 + 65t + 16t2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(160 + 65t + 16t2)' equal to zero and attempt to solve: Simplifying 160 + 65t + 16t2 = 0 Solving 160 + 65t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 10 + 4.0625t + t2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + 4.0625t + -10 + t2 = 0 + -10 Reorder the terms: 10 + -10 + 4.0625t + t2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 4.0625t + t2 = 0 + -10 4.0625t + t2 = 0 + -10 Combine like terms: 0 + -10 = -10 4.0625t + t2 = -10 The t term is 4.0625t. Take half its coefficient (2.03125). Square it (4.125976563) and add it to both sides. Add '4.125976563' to each side of the equation. 4.0625t + 4.125976563 + t2 = -10 + 4.125976563 Reorder the terms: 4.125976563 + 4.0625t + t2 = -10 + 4.125976563 Combine like terms: -10 + 4.125976563 = -5.874023437 4.125976563 + 4.0625t + t2 = -5.874023437 Factor a perfect square on the left side: (t + 2.03125)(t + 2.03125) = -5.874023437 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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