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Simplifying 5t2 + 10t + 50 = 0 Reorder the terms: 50 + 10t + 5t2 = 0 Solving 50 + 10t + 5t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '5'. 5(10 + 2t + t2) = 0 Ignore the factor 5.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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