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Simplifying 592 = -16t2 + 64t + 512 Reorder the terms: 592 = 512 + 64t + -16t2 Solving 592 = 512 + 64t + -16t2 Solving for variable 't'. Combine like terms: 592 + -512 = 80 80 + -64t + 16t2 = 512 + 64t + -16t2 + -512 + -64t + 16t2 Reorder the terms: 80 + -64t + 16t2 = 512 + -512 + 64t + -64t + -16t2 + 16t2 Combine like terms: 512 + -512 = 0 80 + -64t + 16t2 = 0 + 64t + -64t + -16t2 + 16t2 80 + -64t + 16t2 = 64t + -64t + -16t2 + 16t2 Combine like terms: 64t + -64t = 0 80 + -64t + 16t2 = 0 + -16t2 + 16t2 80 + -64t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 80 + -64t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(5 + -4t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(5 + -4t + t2)' equal to zero and attempt to solve: Simplifying 5 + -4t + t2 = 0 Solving 5 + -4t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -4t + -5 + t2 = 0 + -5 Reorder the terms: 5 + -5 + -4t + t2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4t + t2 = 0 + -5 -4t + t2 = 0 + -5 Combine like terms: 0 + -5 = -5 -4t + t2 = -5 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 = -5 + 4 Reorder the terms: 4 + -4t + t2 = -5 + 4 Combine like terms: -5 + 4 = -1 4 + -4t + t2 = -1 Factor a perfect square on the left side: (t + -2)(t + -2) = -1 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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