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Simplifying -32T2 + 64T + -400 = 0 Reorder the terms: -400 + 64T + -32T2 = 0 Solving -400 + 64T + -32T2 = 0 Solving for variable 'T'. Factor out the Greatest Common Factor (GCF), '16'. 16(-25 + 4T + -2T2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-25 + 4T + -2T2)' equal to zero and attempt to solve: Simplifying -25 + 4T + -2T2 = 0 Solving -25 + 4T + -2T2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 12.5 + -2T + T2 = 0 Move the constant term to the right: Add '-12.5' to each side of the equation. 12.5 + -2T + -12.5 + T2 = 0 + -12.5 Reorder the terms: 12.5 + -12.5 + -2T + T2 = 0 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + -2T + T2 = 0 + -12.5 -2T + T2 = 0 + -12.5 Combine like terms: 0 + -12.5 = -12.5 -2T + T2 = -12.5 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 = -12.5 + 1 Reorder the terms: 1 + -2T + T2 = -12.5 + 1 Combine like terms: -12.5 + 1 = -11.5 1 + -2T + T2 = -11.5 Factor a perfect square on the left side: (T + -1)(T + -1) = -11.5 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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