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Simplifying 64 = 6t + -4t2 Solving 64 = 6t + -4t2 Solving for variable 't'. Reorder the terms: 64 + -6t + 4t2 = 6t + -6t + -4t2 + 4t2 Combine like terms: 6t + -6t = 0 64 + -6t + 4t2 = 0 + -4t2 + 4t2 64 + -6t + 4t2 = -4t2 + 4t2 Combine like terms: -4t2 + 4t2 = 0 64 + -6t + 4t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(32 + -3t + 2t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(32 + -3t + 2t2)' equal to zero and attempt to solve: Simplifying 32 + -3t + 2t2 = 0 Solving 32 + -3t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 16 + -1.5t + t2 = 0 Move the constant term to the right: Add '-16' to each side of the equation. 16 + -1.5t + -16 + t2 = 0 + -16 Reorder the terms: 16 + -16 + -1.5t + t2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -1.5t + t2 = 0 + -16 -1.5t + t2 = 0 + -16 Combine like terms: 0 + -16 = -16 -1.5t + t2 = -16 The t term is -1.5t. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5t + 0.5625 + t2 = -16 + 0.5625 Reorder the terms: 0.5625 + -1.5t + t2 = -16 + 0.5625 Combine like terms: -16 + 0.5625 = -15.4375 0.5625 + -1.5t + t2 = -15.4375 Factor a perfect square on the left side: (t + -0.75)(t + -0.75) = -15.4375 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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