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Simplifying -16t2 + 112t = 208 Reorder the terms: 112t + -16t2 = 208 Solving 112t + -16t2 = 208 Solving for variable 't'. Reorder the terms: -208 + 112t + -16t2 = 208 + -208 Combine like terms: 208 + -208 = 0 -208 + 112t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-13 + 7t + -1t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-13 + 7t + -1t2)' equal to zero and attempt to solve: Simplifying -13 + 7t + -1t2 = 0 Solving -13 + 7t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 13 + -7t + t2 = 0 Move the constant term to the right: Add '-13' to each side of the equation. 13 + -7t + -13 + t2 = 0 + -13 Reorder the terms: 13 + -13 + -7t + t2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -7t + t2 = 0 + -13 -7t + t2 = 0 + -13 Combine like terms: 0 + -13 = -13 -7t + t2 = -13 The t term is -7t. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7t + 12.25 + t2 = -13 + 12.25 Reorder the terms: 12.25 + -7t + t2 = -13 + 12.25 Combine like terms: -13 + 12.25 = -0.75 12.25 + -7t + t2 = -0.75 Factor a perfect square on the left side: (t + -3.5)(t + -3.5) = -0.75 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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