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Simplifying (3t2 + 6t + -1) + (5t2 + 4t + 7) = 0 Reorder the terms: (-1 + 6t + 3t2) + (5t2 + 4t + 7) = 0 Remove parenthesis around (-1 + 6t + 3t2) -1 + 6t + 3t2 + (5t2 + 4t + 7) = 0 Reorder the terms: -1 + 6t + 3t2 + (7 + 4t + 5t2) = 0 Remove parenthesis around (7 + 4t + 5t2) -1 + 6t + 3t2 + 7 + 4t + 5t2 = 0 Reorder the terms: -1 + 7 + 6t + 4t + 3t2 + 5t2 = 0 Combine like terms: -1 + 7 = 6 6 + 6t + 4t + 3t2 + 5t2 = 0 Combine like terms: 6t + 4t = 10t 6 + 10t + 3t2 + 5t2 = 0 Combine like terms: 3t2 + 5t2 = 8t2 6 + 10t + 8t2 = 0 Solving 6 + 10t + 8t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 5t + 4t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 5t + 4t2)' equal to zero and attempt to solve: Simplifying 3 + 5t + 4t2 = 0 Solving 3 + 5t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.75 + 1.25t + t2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + 1.25t + -0.75 + t2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + 1.25t + t2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 1.25t + t2 = 0 + -0.75 1.25t + t2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 1.25t + t2 = -0.75 The t term is 1.25t. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25t + 0.390625 + t2 = -0.75 + 0.390625 Reorder the terms: 0.390625 + 1.25t + t2 = -0.75 + 0.390625 Combine like terms: -0.75 + 0.390625 = -0.359375 0.390625 + 1.25t + t2 = -0.359375 Factor a perfect square on the left side: (t + 0.625)(t + 0.625) = -0.359375 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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