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Simplifying 3t(t + 4) + -3 = 3t(3t) + 9t Reorder the terms: 3t(4 + t) + -3 = 3t(3t) + 9t (4 * 3t + t * 3t) + -3 = 3t(3t) + 9t (12t + 3t2) + -3 = 3t(3t) + 9t Reorder the terms: -3 + 12t + 3t2 = 3t(3t) + 9t Remove parenthesis around (3t) -3 + 12t + 3t2 = 3t * 3t + 9t Reorder the terms for easier multiplication: -3 + 12t + 3t2 = 3 * 3t * t + 9t Multiply 3 * 3 -3 + 12t + 3t2 = 9t * t + 9t Multiply t * t -3 + 12t + 3t2 = 9t2 + 9t Reorder the terms: -3 + 12t + 3t2 = 9t + 9t2 Solving -3 + 12t + 3t2 = 9t + 9t2 Solving for variable 't'. Reorder the terms: -3 + 12t + -9t + 3t2 + -9t2 = 9t + 9t2 + -9t + -9t2 Combine like terms: 12t + -9t = 3t -3 + 3t + 3t2 + -9t2 = 9t + 9t2 + -9t + -9t2 Combine like terms: 3t2 + -9t2 = -6t2 -3 + 3t + -6t2 = 9t + 9t2 + -9t + -9t2 Reorder the terms: -3 + 3t + -6t2 = 9t + -9t + 9t2 + -9t2 Combine like terms: 9t + -9t = 0 -3 + 3t + -6t2 = 0 + 9t2 + -9t2 -3 + 3t + -6t2 = 9t2 + -9t2 Combine like terms: 9t2 + -9t2 = 0 -3 + 3t + -6t2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + t + -2t2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + t + -2t2)' equal to zero and attempt to solve: Simplifying -1 + t + -2t2 = 0 Solving -1 + t + -2t2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 0.5 + -0.5t + t2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -0.5t + -0.5 + t2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -0.5t + t2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -0.5t + t2 = 0 + -0.5 -0.5t + t2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -0.5t + t2 = -0.5 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.5t + 0.25 + t2 = -0.5 + 0.25 Reorder the terms: 0.25 + -0.5t + t2 = -0.5 + 0.25 Combine like terms: -0.5 + 0.25 = -0.25 0.25 + -0.5t + t2 = -0.25 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = -0.25 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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