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Simplifying 4 = -16t2 + 14t + 0 Reorder the terms: 4 = 0 + 14t + -16t2 Remove the zero: 4 = 14t + -16t2 Solving 4 = 14t + -16t2 Solving for variable 't'. Reorder the terms: 4 + -14t + 16t2 = 14t + -14t + -16t2 + 16t2 Combine like terms: 14t + -14t = 0 4 + -14t + 16t2 = 0 + -16t2 + 16t2 4 + -14t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 4 + -14t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2 + -7t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -7t + 8t2)' equal to zero and attempt to solve: Simplifying 2 + -7t + 8t2 = 0 Solving 2 + -7t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.25 + -0.875t + t2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -0.875t + -0.25 + t2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -0.875t + t2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -0.875t + t2 = 0 + -0.25 -0.875t + t2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -0.875t + t2 = -0.25 The t term is -0.875t. Take half its coefficient (-0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. -0.875t + 0.19140625 + t2 = -0.25 + 0.19140625 Reorder the terms: 0.19140625 + -0.875t + t2 = -0.25 + 0.19140625 Combine like terms: -0.25 + 0.19140625 = -0.05859375 0.19140625 + -0.875t + t2 = -0.05859375 Factor a perfect square on the left side: (t + -0.4375)(t + -0.4375) = -0.05859375 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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