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Simplifying 0 = 16t2 + 12t + 10 Reorder the terms: 0 = 10 + 12t + 16t2 Solving 0 = 10 + 12t + 16t2 Solving for variable 't'. Combine like terms: 0 + -10 = -10 -10 + -12t + -16t2 = 10 + 12t + 16t2 + -10 + -12t + -16t2 Reorder the terms: -10 + -12t + -16t2 = 10 + -10 + 12t + -12t + 16t2 + -16t2 Combine like terms: 10 + -10 = 0 -10 + -12t + -16t2 = 0 + 12t + -12t + 16t2 + -16t2 -10 + -12t + -16t2 = 12t + -12t + 16t2 + -16t2 Combine like terms: 12t + -12t = 0 -10 + -12t + -16t2 = 0 + 16t2 + -16t2 -10 + -12t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -10 + -12t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(5 + 6t + 8t2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(5 + 6t + 8t2)' equal to zero and attempt to solve: Simplifying 5 + 6t + 8t2 = 0 Solving 5 + 6t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.625 + 0.75t + t2 = 0 Move the constant term to the right: Add '-0.625' to each side of the equation. 0.625 + 0.75t + -0.625 + t2 = 0 + -0.625 Reorder the terms: 0.625 + -0.625 + 0.75t + t2 = 0 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + 0.75t + t2 = 0 + -0.625 0.75t + t2 = 0 + -0.625 Combine like terms: 0 + -0.625 = -0.625 0.75t + t2 = -0.625 The t term is 0.75t. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75t + 0.140625 + t2 = -0.625 + 0.140625 Reorder the terms: 0.140625 + 0.75t + t2 = -0.625 + 0.140625 Combine like terms: -0.625 + 0.140625 = -0.484375 0.140625 + 0.75t + t2 = -0.484375 Factor a perfect square on the left side: (t + 0.375)(t + 0.375) = -0.484375 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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