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Simplifying 0 = 100 + 5t + 4t2 Solving 0 = 100 + 5t + 4t2 Solving for variable 't'. Combine like terms: 0 + -100 = -100 -100 + -5t + -4t2 = 100 + 5t + 4t2 + -100 + -5t + -4t2 Reorder the terms: -100 + -5t + -4t2 = 100 + -100 + 5t + -5t + 4t2 + -4t2 Combine like terms: 100 + -100 = 0 -100 + -5t + -4t2 = 0 + 5t + -5t + 4t2 + -4t2 -100 + -5t + -4t2 = 5t + -5t + 4t2 + -4t2 Combine like terms: 5t + -5t = 0 -100 + -5t + -4t2 = 0 + 4t2 + -4t2 -100 + -5t + -4t2 = 4t2 + -4t2 Combine like terms: 4t2 + -4t2 = 0 -100 + -5t + -4t2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(100 + 5t + 4t2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(100 + 5t + 4t2)' equal to zero and attempt to solve: Simplifying 100 + 5t + 4t2 = 0 Solving 100 + 5t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 25 + 1.25t + t2 = 0 Move the constant term to the right: Add '-25' to each side of the equation. 25 + 1.25t + -25 + t2 = 0 + -25 Reorder the terms: 25 + -25 + 1.25t + t2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 1.25t + t2 = 0 + -25 1.25t + t2 = 0 + -25 Combine like terms: 0 + -25 = -25 1.25t + t2 = -25 The t term is 1.25t. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25t + 0.390625 + t2 = -25 + 0.390625 Reorder the terms: 0.390625 + 1.25t + t2 = -25 + 0.390625 Combine like terms: -25 + 0.390625 = -24.609375 0.390625 + 1.25t + t2 = -24.609375 Factor a perfect square on the left side: (t + 0.625)(t + 0.625) = -24.609375 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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