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Simplifying -32t2 + -48t + -24 = 0 Reorder the terms: -24 + -48t + -32t2 = 0 Solving -24 + -48t + -32t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '-8'. -8(3 + 6t + 4t2) = 0 Ignore the factor -8.Subproblem 1
Set the factor '(3 + 6t + 4t2)' equal to zero and attempt to solve: Simplifying 3 + 6t + 4t2 = 0 Solving 3 + 6t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.75 + 1.5t + t2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + 1.5t + -0.75 + t2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + 1.5t + t2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 1.5t + t2 = 0 + -0.75 1.5t + t2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 1.5t + t2 = -0.75 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 = -0.75 + 0.5625 Reorder the terms: 0.5625 + 1.5t + t2 = -0.75 + 0.5625 Combine like terms: -0.75 + 0.5625 = -0.1875 0.5625 + 1.5t + t2 = -0.1875 Factor a perfect square on the left side: (t + 0.75)(t + 0.75) = -0.1875 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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