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Simplifying 0 = 16t2 + 4t + 35 Reorder the terms: 0 = 35 + 4t + 16t2 Solving 0 = 35 + 4t + 16t2 Solving for variable 't'. Combine like terms: 0 + -35 = -35 -35 + -4t + -16t2 = 35 + 4t + 16t2 + -35 + -4t + -16t2 Reorder the terms: -35 + -4t + -16t2 = 35 + -35 + 4t + -4t + 16t2 + -16t2 Combine like terms: 35 + -35 = 0 -35 + -4t + -16t2 = 0 + 4t + -4t + 16t2 + -16t2 -35 + -4t + -16t2 = 4t + -4t + 16t2 + -16t2 Combine like terms: 4t + -4t = 0 -35 + -4t + -16t2 = 0 + 16t2 + -16t2 -35 + -4t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -35 + -4t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(35 + 4t + 16t2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(35 + 4t + 16t2)' equal to zero and attempt to solve: Simplifying 35 + 4t + 16t2 = 0 Solving 35 + 4t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 2.1875 + 0.25t + t2 = 0 Move the constant term to the right: Add '-2.1875' to each side of the equation. 2.1875 + 0.25t + -2.1875 + t2 = 0 + -2.1875 Reorder the terms: 2.1875 + -2.1875 + 0.25t + t2 = 0 + -2.1875 Combine like terms: 2.1875 + -2.1875 = 0.0000 0.0000 + 0.25t + t2 = 0 + -2.1875 0.25t + t2 = 0 + -2.1875 Combine like terms: 0 + -2.1875 = -2.1875 0.25t + t2 = -2.1875 The t term is 0.25t. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25t + 0.015625 + t2 = -2.1875 + 0.015625 Reorder the terms: 0.015625 + 0.25t + t2 = -2.1875 + 0.015625 Combine like terms: -2.1875 + 0.015625 = -2.171875 0.015625 + 0.25t + t2 = -2.171875 Factor a perfect square on the left side: (t + 0.125)(t + 0.125) = -2.171875 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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