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Simplifying 42 = -16t2 + 42t + 6 Reorder the terms: 42 = 6 + 42t + -16t2 Solving 42 = 6 + 42t + -16t2 Solving for variable 't'. Combine like terms: 42 + -6 = 36 36 + -42t + 16t2 = 6 + 42t + -16t2 + -6 + -42t + 16t2 Reorder the terms: 36 + -42t + 16t2 = 6 + -6 + 42t + -42t + -16t2 + 16t2 Combine like terms: 6 + -6 = 0 36 + -42t + 16t2 = 0 + 42t + -42t + -16t2 + 16t2 36 + -42t + 16t2 = 42t + -42t + -16t2 + 16t2 Combine like terms: 42t + -42t = 0 36 + -42t + 16t2 = 0 + -16t2 + 16t2 36 + -42t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 36 + -42t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(18 + -21t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(18 + -21t + 8t2)' equal to zero and attempt to solve: Simplifying 18 + -21t + 8t2 = 0 Solving 18 + -21t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 2.25 + -2.625t + t2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + -2.625t + -2.25 + t2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + -2.625t + t2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + -2.625t + t2 = 0 + -2.25 -2.625t + t2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 -2.625t + t2 = -2.25 The t term is -2.625t. Take half its coefficient (-1.3125). Square it (1.72265625) and add it to both sides. Add '1.72265625' to each side of the equation. -2.625t + 1.72265625 + t2 = -2.25 + 1.72265625 Reorder the terms: 1.72265625 + -2.625t + t2 = -2.25 + 1.72265625 Combine like terms: -2.25 + 1.72265625 = -0.52734375 1.72265625 + -2.625t + t2 = -0.52734375 Factor a perfect square on the left side: (t + -1.3125)(t + -1.3125) = -0.52734375 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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