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Simplifying 160 = -16t2 + 32t + 128 Reorder the terms: 160 = 128 + 32t + -16t2 Solving 160 = 128 + 32t + -16t2 Solving for variable 't'. Combine like terms: 160 + -128 = 32 32 + -32t + 16t2 = 128 + 32t + -16t2 + -128 + -32t + 16t2 Reorder the terms: 32 + -32t + 16t2 = 128 + -128 + 32t + -32t + -16t2 + 16t2 Combine like terms: 128 + -128 = 0 32 + -32t + 16t2 = 0 + 32t + -32t + -16t2 + 16t2 32 + -32t + 16t2 = 32t + -32t + -16t2 + 16t2 Combine like terms: 32t + -32t = 0 32 + -32t + 16t2 = 0 + -16t2 + 16t2 32 + -32t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 32 + -32t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(2 + -2t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(2 + -2t + t2)' equal to zero and attempt to solve: Simplifying 2 + -2t + t2 = 0 Solving 2 + -2t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -2t + -2 + t2 = 0 + -2 Reorder the terms: 2 + -2 + -2t + t2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -2t + t2 = 0 + -2 -2t + t2 = 0 + -2 Combine like terms: 0 + -2 = -2 -2t + t2 = -2 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 = -2 + 1 Reorder the terms: 1 + -2t + t2 = -2 + 1 Combine like terms: -2 + 1 = -1 1 + -2t + t2 = -1 Factor a perfect square on the left side: (t + -1)(t + -1) = -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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