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Simplifying 0 = 4t2 + 3t + 2 Reorder the terms: 0 = 2 + 3t + 4t2 Solving 0 = 2 + 3t + 4t2 Solving for variable 't'. Combine like terms: 0 + -2 = -2 -2 + -3t + -4t2 = 2 + 3t + 4t2 + -2 + -3t + -4t2 Reorder the terms: -2 + -3t + -4t2 = 2 + -2 + 3t + -3t + 4t2 + -4t2 Combine like terms: 2 + -2 = 0 -2 + -3t + -4t2 = 0 + 3t + -3t + 4t2 + -4t2 -2 + -3t + -4t2 = 3t + -3t + 4t2 + -4t2 Combine like terms: 3t + -3t = 0 -2 + -3t + -4t2 = 0 + 4t2 + -4t2 -2 + -3t + -4t2 = 4t2 + -4t2 Combine like terms: 4t2 + -4t2 = 0 -2 + -3t + -4t2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(2 + 3t + 4t2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + 3t + 4t2)' equal to zero and attempt to solve: Simplifying 2 + 3t + 4t2 = 0 Solving 2 + 3t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.5 + 0.75t + t2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 0.75t + -0.5 + t2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 0.75t + t2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 0.75t + t2 = 0 + -0.5 0.75t + t2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 0.75t + t2 = -0.5 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 = -0.5 + 0.140625 Reorder the terms: 0.140625 + 0.75t + t2 = -0.5 + 0.140625 Combine like terms: -0.5 + 0.140625 = -0.359375 0.140625 + 0.75t + t2 = -0.359375 Factor a perfect square on the left side: (t + 0.375)(t + 0.375) = -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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