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Simplifying 5t2 + 30t + 100 = 0 Reorder the terms: 100 + 30t + 5t2 = 0 Solving 100 + 30t + 5t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '5'. 5(20 + 6t + t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(20 + 6t + t2)' equal to zero and attempt to solve: Simplifying 20 + 6t + t2 = 0 Solving 20 + 6t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + 6t + -20 + t2 = 0 + -20 Reorder the terms: 20 + -20 + 6t + t2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 6t + t2 = 0 + -20 6t + t2 = 0 + -20 Combine like terms: 0 + -20 = -20 6t + t2 = -20 The t term is 6t. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6t + 9 + t2 = -20 + 9 Reorder the terms: 9 + 6t + t2 = -20 + 9 Combine like terms: -20 + 9 = -11 9 + 6t + t2 = -11 Factor a perfect square on the left side: (t + 3)(t + 3) = -11 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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