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Simplifying 48 = 16t2 + 32t + 320 Reorder the terms: 48 = 320 + 32t + 16t2 Solving 48 = 320 + 32t + 16t2 Solving for variable 't'. Combine like terms: 48 + -320 = -272 -272 + -32t + -16t2 = 320 + 32t + 16t2 + -320 + -32t + -16t2 Reorder the terms: -272 + -32t + -16t2 = 320 + -320 + 32t + -32t + 16t2 + -16t2 Combine like terms: 320 + -320 = 0 -272 + -32t + -16t2 = 0 + 32t + -32t + 16t2 + -16t2 -272 + -32t + -16t2 = 32t + -32t + 16t2 + -16t2 Combine like terms: 32t + -32t = 0 -272 + -32t + -16t2 = 0 + 16t2 + -16t2 -272 + -32t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -272 + -32t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-16'. -16(17 + 2t + t2) = 0 Ignore the factor -16.Subproblem 1
Set the factor '(17 + 2t + t2)' equal to zero and attempt to solve: Simplifying 17 + 2t + t2 = 0 Solving 17 + 2t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + 2t + -17 + t2 = 0 + -17 Reorder the terms: 17 + -17 + 2t + t2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 2t + t2 = 0 + -17 2t + t2 = 0 + -17 Combine like terms: 0 + -17 = -17 2t + t2 = -17 The t term is 2t. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2t + 1 + t2 = -17 + 1 Reorder the terms: 1 + 2t + t2 = -17 + 1 Combine like terms: -17 + 1 = -16 1 + 2t + t2 = -16 Factor a perfect square on the left side: (t + 1)(t + 1) = -16 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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