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Simplifying 0 = 16t2 + 64t + 512 Reorder the terms: 0 = 512 + 64t + 16t2 Solving 0 = 512 + 64t + 16t2 Solving for variable 't'. Combine like terms: 0 + -512 = -512 -512 + -64t + -16t2 = 512 + 64t + 16t2 + -512 + -64t + -16t2 Reorder the terms: -512 + -64t + -16t2 = 512 + -512 + 64t + -64t + 16t2 + -16t2 Combine like terms: 512 + -512 = 0 -512 + -64t + -16t2 = 0 + 64t + -64t + 16t2 + -16t2 -512 + -64t + -16t2 = 64t + -64t + 16t2 + -16t2 Combine like terms: 64t + -64t = 0 -512 + -64t + -16t2 = 0 + 16t2 + -16t2 -512 + -64t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -512 + -64t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-16'. -16(32 + 4t + t2) = 0 Ignore the factor -16.Subproblem 1
Set the factor '(32 + 4t + t2)' equal to zero and attempt to solve: Simplifying 32 + 4t + t2 = 0 Solving 32 + 4t + t2 = 0 Begin completing the square. 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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