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Simplifying 0 = 6t2 + 64t + 192 Reorder the terms: 0 = 192 + 64t + 6t2 Solving 0 = 192 + 64t + 6t2 Solving for variable 't'. Combine like terms: 0 + -192 = -192 -192 + -64t + -6t2 = 192 + 64t + 6t2 + -192 + -64t + -6t2 Reorder the terms: -192 + -64t + -6t2 = 192 + -192 + 64t + -64t + 6t2 + -6t2 Combine like terms: 192 + -192 = 0 -192 + -64t + -6t2 = 0 + 64t + -64t + 6t2 + -6t2 -192 + -64t + -6t2 = 64t + -64t + 6t2 + -6t2 Combine like terms: 64t + -64t = 0 -192 + -64t + -6t2 = 0 + 6t2 + -6t2 -192 + -64t + -6t2 = 6t2 + -6t2 Combine like terms: 6t2 + -6t2 = 0 -192 + -64t + -6t2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(96 + 32t + 3t2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(96 + 32t + 3t2)' equal to zero and attempt to solve: Simplifying 96 + 32t + 3t2 = 0 Solving 96 + 32t + 3t2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 32 + 10.66666667t + t2 = 0 Move the constant term to the right: Add '-32' to each side of the equation. 32 + 10.66666667t + -32 + t2 = 0 + -32 Reorder the terms: 32 + -32 + 10.66666667t + t2 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + 10.66666667t + t2 = 0 + -32 10.66666667t + t2 = 0 + -32 Combine like terms: 0 + -32 = -32 10.66666667t + t2 = -32 The t term is 10.66666667t. Take half its coefficient (5.333333335). Square it (28.44444446) and add it to both sides. Add '28.44444446' to each side of the equation. 10.66666667t + 28.44444446 + t2 = -32 + 28.44444446 Reorder the terms: 28.44444446 + 10.66666667t + t2 = -32 + 28.44444446 Combine like terms: -32 + 28.44444446 = -3.55555554 28.44444446 + 10.66666667t + t2 = -3.55555554 Factor a perfect square on the left side: (t + 5.333333335)(t + 5.333333335) = -3.55555554 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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