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Simplifying 6t2 + 64 = 4t Reorder the terms: 64 + 6t2 = 4t Solving 64 + 6t2 = 4t Solving for variable 't'. Reorder the terms: 64 + -4t + 6t2 = 4t + -4t Combine like terms: 4t + -4t = 0 64 + -4t + 6t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(32 + -2t + 3t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(32 + -2t + 3t2)' equal to zero and attempt to solve: Simplifying 32 + -2t + 3t2 = 0 Solving 32 + -2t + 3t2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 10.66666667 + -0.6666666667t + t2 = 0 Move the constant term to the right: Add '-10.66666667' to each side of the equation. 10.66666667 + -0.6666666667t + -10.66666667 + t2 = 0 + -10.66666667 Reorder the terms: 10.66666667 + -10.66666667 + -0.6666666667t + t2 = 0 + -10.66666667 Combine like terms: 10.66666667 + -10.66666667 = 0.00000000 0.00000000 + -0.6666666667t + t2 = 0 + -10.66666667 -0.6666666667t + t2 = 0 + -10.66666667 Combine like terms: 0 + -10.66666667 = -10.66666667 -0.6666666667t + t2 = -10.66666667 The t term is -0.6666666667t. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667t + 0.1111111112 + t2 = -10.66666667 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667t + t2 = -10.66666667 + 0.1111111112 Combine like terms: -10.66666667 + 0.1111111112 = -10.5555555588 0.1111111112 + -0.6666666667t + t2 = -10.5555555588 Factor a perfect square on the left side: (t + -0.3333333334)(t + -0.3333333334) = -10.5555555588 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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