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Simplifying 160 = -16t2 + 32t Reorder the terms: 160 = 32t + -16t2 Solving 160 = 32t + -16t2 Solving for variable 't'. Reorder the terms: 160 + -32t + 16t2 = 32t + -32t + -16t2 + 16t2 Combine like terms: 32t + -32t = 0 160 + -32t + 16t2 = 0 + -16t2 + 16t2 160 + -32t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 160 + -32t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(10 + -2t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(10 + -2t + t2)' equal to zero and attempt to solve: Simplifying 10 + -2t + t2 = 0 Solving 10 + -2t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + -2t + -10 + t2 = 0 + -10 Reorder the terms: 10 + -10 + -2t + t2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -2t + t2 = 0 + -10 -2t + t2 = 0 + -10 Combine like terms: 0 + -10 = -10 -2t + t2 = -10 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 = -10 + 1 Reorder the terms: 1 + -2t + t2 = -10 + 1 Combine like terms: -10 + 1 = -9 1 + -2t + t2 = -9 Factor a perfect square on the left side: (t + -1)(t + -1) = -9 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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