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Simplifying 0 = 4t2 + -24t + 100 Reorder the terms: 0 = 100 + -24t + 4t2 Solving 0 = 100 + -24t + 4t2 Solving for variable 't'. Combine like terms: 0 + -100 = -100 -100 + 24t + -4t2 = 100 + -24t + 4t2 + -100 + 24t + -4t2 Reorder the terms: -100 + 24t + -4t2 = 100 + -100 + -24t + 24t + 4t2 + -4t2 Combine like terms: 100 + -100 = 0 -100 + 24t + -4t2 = 0 + -24t + 24t + 4t2 + -4t2 -100 + 24t + -4t2 = -24t + 24t + 4t2 + -4t2 Combine like terms: -24t + 24t = 0 -100 + 24t + -4t2 = 0 + 4t2 + -4t2 -100 + 24t + -4t2 = 4t2 + -4t2 Combine like terms: 4t2 + -4t2 = 0 -100 + 24t + -4t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-25 + 6t + -1t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-25 + 6t + -1t2)' equal to zero and attempt to solve: Simplifying -25 + 6t + -1t2 = 0 Solving -25 + 6t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 25 + -6t + t2 = 0 Move the constant term to the right: Add '-25' to each side of the equation. 25 + -6t + -25 + t2 = 0 + -25 Reorder the terms: 25 + -25 + -6t + t2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -6t + t2 = 0 + -25 -6t + t2 = 0 + -25 Combine like terms: 0 + -25 = -25 -6t + t2 = -25 The t term is -6t. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6t + 9 + t2 = -25 + 9 Reorder the terms: 9 + -6t + t2 = -25 + 9 Combine like terms: -25 + 9 = -16 9 + -6t + t2 = -16 Factor a perfect square on the left side: (t + -3)(t + -3) = -16 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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