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Simplifying 4t2 + 16t = -120 Reorder the terms: 16t + 4t2 = -120 Solving 16t + 4t2 = -120 Solving for variable 't'. Reorder the terms: 120 + 16t + 4t2 = -120 + 120 Combine like terms: -120 + 120 = 0 120 + 16t + 4t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(30 + 4t + t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(30 + 4t + t2)' equal to zero and attempt to solve: Simplifying 30 + 4t + t2 = 0 Solving 30 + 4t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + 4t + -30 + t2 = 0 + -30 Reorder the terms: 30 + -30 + 4t + t2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + 4t + t2 = 0 + -30 4t + t2 = 0 + -30 Combine like terms: 0 + -30 = -30 4t + t2 = -30 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 = -30 + 4 Reorder the terms: 4 + 4t + t2 = -30 + 4 Combine like terms: -30 + 4 = -26 4 + 4t + t2 = -26 Factor a perfect square on the left side: (t + 2)(t + 2) = -26 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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