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Simplifying 12t2 + -9t + 10 + (6t + 2) = 0 Reorder the terms: 12t2 + -9t + 10 + (2 + 6t) = 0 Remove parenthesis around (2 + 6t) 12t2 + -9t + 10 + 2 + 6t = 0 Reorder the terms: 10 + 2 + -9t + 6t + 12t2 = 0 Combine like terms: 10 + 2 = 12 12 + -9t + 6t + 12t2 = 0 Combine like terms: -9t + 6t = -3t 12 + -3t + 12t2 = 0 Solving 12 + -3t + 12t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '3'. 3(4 + -1t + 4t2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + -1t + 4t2)' equal to zero and attempt to solve: Simplifying 4 + -1t + 4t2 = 0 Solving 4 + -1t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1 + -0.25t + t2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -0.25t + -1 + t2 = 0 + -1 Reorder the terms: 1 + -1 + -0.25t + t2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -0.25t + t2 = 0 + -1 -0.25t + t2 = 0 + -1 Combine like terms: 0 + -1 = -1 -0.25t + t2 = -1 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 = -1 + 0.015625 Reorder the terms: 0.015625 + -0.25t + t2 = -1 + 0.015625 Combine like terms: -1 + 0.015625 = -0.984375 0.015625 + -0.25t + t2 = -0.984375 Factor a perfect square on the left side: (t + -0.125)(t + -0.125) = -0.984375 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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