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Simplifying 40 = -16t2 + 36t Reorder the terms: 40 = 36t + -16t2 Solving 40 = 36t + -16t2 Solving for variable 't'. Reorder the terms: 40 + -36t + 16t2 = 36t + -36t + -16t2 + 16t2 Combine like terms: 36t + -36t = 0 40 + -36t + 16t2 = 0 + -16t2 + 16t2 40 + -36t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 40 + -36t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(10 + -9t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(10 + -9t + 4t2)' equal to zero and attempt to solve: Simplifying 10 + -9t + 4t2 = 0 Solving 10 + -9t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.5 + -2.25t + t2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -2.25t + -2.5 + t2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -2.25t + t2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -2.25t + t2 = 0 + -2.5 -2.25t + t2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -2.25t + t2 = -2.5 The t term is -2.25t. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25t + 1.265625 + t2 = -2.5 + 1.265625 Reorder the terms: 1.265625 + -2.25t + t2 = -2.5 + 1.265625 Combine like terms: -2.5 + 1.265625 = -1.234375 1.265625 + -2.25t + t2 = -1.234375 Factor a perfect square on the left side: (t + -1.125)(t + -1.125) = -1.234375 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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