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Simplifying 560 = -16t2 + 16t + 512 Reorder the terms: 560 = 512 + 16t + -16t2 Solving 560 = 512 + 16t + -16t2 Solving for variable 't'. Combine like terms: 560 + -512 = 48 48 + -16t + 16t2 = 512 + 16t + -16t2 + -512 + -16t + 16t2 Reorder the terms: 48 + -16t + 16t2 = 512 + -512 + 16t + -16t + -16t2 + 16t2 Combine like terms: 512 + -512 = 0 48 + -16t + 16t2 = 0 + 16t + -16t + -16t2 + 16t2 48 + -16t + 16t2 = 16t + -16t + -16t2 + 16t2 Combine like terms: 16t + -16t = 0 48 + -16t + 16t2 = 0 + -16t2 + 16t2 48 + -16t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 48 + -16t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(3 + -1t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(3 + -1t + t2)' equal to zero and attempt to solve: Simplifying 3 + -1t + t2 = 0 Solving 3 + -1t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -1t + -3 + t2 = 0 + -3 Reorder the terms: 3 + -3 + -1t + t2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1t + t2 = 0 + -3 -1t + t2 = 0 + -3 Combine like terms: 0 + -3 = -3 -1t + t2 = -3 The t term is -1t. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1t + 0.25 + t2 = -3 + 0.25 Reorder the terms: 0.25 + -1t + t2 = -3 + 0.25 Combine like terms: -3 + 0.25 = -2.75 0.25 + -1t + t2 = -2.75 Factor a perfect square on the left side: (t + -0.5)(t + -0.5) = -2.75 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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