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Simplifying 4 + 9t2 = 6t + -7t2 Solving 4 + 9t2 = 6t + -7t2 Solving for variable 't'. Reorder the terms: 4 + -6t + 9t2 + 7t2 = 6t + -7t2 + -6t + 7t2 Combine like terms: 9t2 + 7t2 = 16t2 4 + -6t + 16t2 = 6t + -7t2 + -6t + 7t2 Reorder the terms: 4 + -6t + 16t2 = 6t + -6t + -7t2 + 7t2 Combine like terms: 6t + -6t = 0 4 + -6t + 16t2 = 0 + -7t2 + 7t2 4 + -6t + 16t2 = -7t2 + 7t2 Combine like terms: -7t2 + 7t2 = 0 4 + -6t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2 + -3t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -3t + 8t2)' equal to zero and attempt to solve: Simplifying 2 + -3t + 8t2 = 0 Solving 2 + -3t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.25 + -0.375t + t2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -0.375t + -0.25 + t2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -0.375t + t2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -0.375t + t2 = 0 + -0.25 -0.375t + t2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -0.375t + t2 = -0.25 The t term is -0.375t. Take half its coefficient (-0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. -0.375t + 0.03515625 + t2 = -0.25 + 0.03515625 Reorder the terms: 0.03515625 + -0.375t + t2 = -0.25 + 0.03515625 Combine like terms: -0.25 + 0.03515625 = -0.21484375 0.03515625 + -0.375t + t2 = -0.21484375 Factor a perfect square on the left side: (t + -0.1875)(t + -0.1875) = -0.21484375 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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