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Simplifying 16t2 + 32t + 224 = 0 Reorder the terms: 224 + 32t + 16t2 = 0 Solving 224 + 32t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16'. 16(14 + 2t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(14 + 2t + t2)' equal to zero and attempt to solve: Simplifying 14 + 2t + t2 = 0 Solving 14 + 2t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + 2t + -14 + t2 = 0 + -14 Reorder the terms: 14 + -14 + 2t + t2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 2t + t2 = 0 + -14 2t + t2 = 0 + -14 Combine like terms: 0 + -14 = -14 2t + t2 = -14 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 = -14 + 1 Reorder the terms: 1 + 2t + t2 = -14 + 1 Combine like terms: -14 + 1 = -13 1 + 2t + t2 = -13 Factor a perfect square on the left side: (t + 1)(t + 1) = -13 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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