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Simplifying 180 = 20t + -5t2 Solving 180 = 20t + -5t2 Solving for variable 't'. Reorder the terms: 180 + -20t + 5t2 = 20t + -20t + -5t2 + 5t2 Combine like terms: 20t + -20t = 0 180 + -20t + 5t2 = 0 + -5t2 + 5t2 180 + -20t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 180 + -20t + 5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(36 + -4t + t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(36 + -4t + t2)' equal to zero and attempt to solve: Simplifying 36 + -4t + t2 = 0 Solving 36 + -4t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + -4t + -36 + t2 = 0 + -36 Reorder the terms: 36 + -36 + -4t + t2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -4t + t2 = 0 + -36 -4t + t2 = 0 + -36 Combine like terms: 0 + -36 = -36 -4t + t2 = -36 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 = -36 + 4 Reorder the terms: 4 + -4t + t2 = -36 + 4 Combine like terms: -36 + 4 = -32 4 + -4t + t2 = -32 Factor a perfect square on the left side: (t + -2)(t + -2) = -32 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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