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Simplifying 0 = 4t2 + -8t + 10 Reorder the terms: 0 = 10 + -8t + 4t2 Solving 0 = 10 + -8t + 4t2 Solving for variable 't'. Combine like terms: 0 + -10 = -10 -10 + 8t + -4t2 = 10 + -8t + 4t2 + -10 + 8t + -4t2 Reorder the terms: -10 + 8t + -4t2 = 10 + -10 + -8t + 8t + 4t2 + -4t2 Combine like terms: 10 + -10 = 0 -10 + 8t + -4t2 = 0 + -8t + 8t + 4t2 + -4t2 -10 + 8t + -4t2 = -8t + 8t + 4t2 + -4t2 Combine like terms: -8t + 8t = 0 -10 + 8t + -4t2 = 0 + 4t2 + -4t2 -10 + 8t + -4t2 = 4t2 + -4t2 Combine like terms: 4t2 + -4t2 = 0 -10 + 8t + -4t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 4t + -2t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + 4t + -2t2)' equal to zero and attempt to solve: Simplifying -5 + 4t + -2t2 = 0 Solving -5 + 4t + -2t2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 2.5 + -2t + t2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -2t + -2.5 + t2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -2t + t2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -2t + t2 = 0 + -2.5 -2t + t2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -2t + t2 = -2.5 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 = -2.5 + 1 Reorder the terms: 1 + -2t + t2 = -2.5 + 1 Combine like terms: -2.5 + 1 = -1.5 1 + -2t + t2 = -1.5 Factor a perfect square on the left side: (t + -1)(t + -1) = -1.5 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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