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Simplifying 250 = -16t2 + 112t + 6 Reorder the terms: 250 = 6 + 112t + -16t2 Solving 250 = 6 + 112t + -16t2 Solving for variable 't'. Combine like terms: 250 + -6 = 244 244 + -112t + 16t2 = 6 + 112t + -16t2 + -6 + -112t + 16t2 Reorder the terms: 244 + -112t + 16t2 = 6 + -6 + 112t + -112t + -16t2 + 16t2 Combine like terms: 6 + -6 = 0 244 + -112t + 16t2 = 0 + 112t + -112t + -16t2 + 16t2 244 + -112t + 16t2 = 112t + -112t + -16t2 + 16t2 Combine like terms: 112t + -112t = 0 244 + -112t + 16t2 = 0 + -16t2 + 16t2 244 + -112t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 244 + -112t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(61 + -28t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(61 + -28t + 4t2)' equal to zero and attempt to solve: Simplifying 61 + -28t + 4t2 = 0 Solving 61 + -28t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 15.25 + -7t + t2 = 0 Move the constant term to the right: Add '-15.25' to each side of the equation. 15.25 + -7t + -15.25 + t2 = 0 + -15.25 Reorder the terms: 15.25 + -15.25 + -7t + t2 = 0 + -15.25 Combine like terms: 15.25 + -15.25 = 0.00 0.00 + -7t + t2 = 0 + -15.25 -7t + t2 = 0 + -15.25 Combine like terms: 0 + -15.25 = -15.25 -7t + t2 = -15.25 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 = -15.25 + 12.25 Reorder the terms: 12.25 + -7t + t2 = -15.25 + 12.25 Combine like terms: -15.25 + 12.25 = -3 12.25 + -7t + t2 = -3 Factor a perfect square on the left side: (t + -3.5)(t + -3.5) = -3 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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