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Simplifying -16t2 + 64t = 512 Reorder the terms: 64t + -16t2 = 512 Solving 64t + -16t2 = 512 Solving for variable 't'. Reorder the terms: -512 + 64t + -16t2 = 512 + -512 Combine like terms: 512 + -512 = 0 -512 + 64t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-32 + 4t + -1t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-32 + 4t + -1t2)' equal to zero and attempt to solve: Simplifying -32 + 4t + -1t2 = 0 Solving -32 + 4t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 32 + -4t + t2 = 0 Move the constant term to the right: Add '-32' to each side of the equation. 32 + -4t + -32 + t2 = 0 + -32 Reorder the terms: 32 + -32 + -4t + t2 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + -4t + t2 = 0 + -32 -4t + t2 = 0 + -32 Combine like terms: 0 + -32 = -32 -4t + t2 = -32 The t term is -4t. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4t + 4 + t2 = -32 + 4 Reorder the terms: 4 + -4t + t2 = -32 + 4 Combine like terms: -32 + 4 = -28 4 + -4t + t2 = -28 Factor a perfect square on the left side: (t + -2)(t + -2) = -28 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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