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Simplifying 4t2 + -8t + 30 = 0 Reorder the terms: 30 + -8t + 4t2 = 0 Solving 30 + -8t + 4t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(15 + -4t + 2t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(15 + -4t + 2t2)' equal to zero and attempt to solve: Simplifying 15 + -4t + 2t2 = 0 Solving 15 + -4t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7.5 + -2t + t2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + -2t + -7.5 + t2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + -2t + t2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + -2t + t2 = 0 + -7.5 -2t + t2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 -2t + t2 = -7.5 The t term is -2t. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2t + 1 + t2 = -7.5 + 1 Reorder the terms: 1 + -2t + t2 = -7.5 + 1 Combine like terms: -7.5 + 1 = -6.5 1 + -2t + t2 = -6.5 Factor a perfect square on the left side: (t + -1)(t + -1) = -6.5 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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