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Simplifying 0 = 16t2 + 10t + 3 Reorder the terms: 0 = 3 + 10t + 16t2 Solving 0 = 3 + 10t + 16t2 Solving for variable 't'. Combine like terms: 0 + -3 = -3 -3 + -10t + -16t2 = 3 + 10t + 16t2 + -3 + -10t + -16t2 Reorder the terms: -3 + -10t + -16t2 = 3 + -3 + 10t + -10t + 16t2 + -16t2 Combine like terms: 3 + -3 = 0 -3 + -10t + -16t2 = 0 + 10t + -10t + 16t2 + -16t2 -3 + -10t + -16t2 = 10t + -10t + 16t2 + -16t2 Combine like terms: 10t + -10t = 0 -3 + -10t + -16t2 = 0 + 16t2 + -16t2 -3 + -10t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -3 + -10t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(3 + 10t + 16t2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3 + 10t + 16t2)' equal to zero and attempt to solve: Simplifying 3 + 10t + 16t2 = 0 Solving 3 + 10t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.1875 + 0.625t + t2 = 0 Move the constant term to the right: Add '-0.1875' to each side of the equation. 0.1875 + 0.625t + -0.1875 + t2 = 0 + -0.1875 Reorder the terms: 0.1875 + -0.1875 + 0.625t + t2 = 0 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + 0.625t + t2 = 0 + -0.1875 0.625t + t2 = 0 + -0.1875 Combine like terms: 0 + -0.1875 = -0.1875 0.625t + t2 = -0.1875 The t term is 0.625t. Take half its coefficient (0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. 0.625t + 0.09765625 + t2 = -0.1875 + 0.09765625 Reorder the terms: 0.09765625 + 0.625t + t2 = -0.1875 + 0.09765625 Combine like terms: -0.1875 + 0.09765625 = -0.08984375 0.09765625 + 0.625t + t2 = -0.08984375 Factor a perfect square on the left side: (t + 0.3125)(t + 0.3125) = -0.08984375 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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