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Simplifying 10 = -16t2 + 10t Reorder the terms: 10 = 10t + -16t2 Solving 10 = 10t + -16t2 Solving for variable 't'. Reorder the terms: 10 + -10t + 16t2 = 10t + -10t + -16t2 + 16t2 Combine like terms: 10t + -10t = 0 10 + -10t + 16t2 = 0 + -16t2 + 16t2 10 + -10t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 10 + -10t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -5t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -5t + 8t2)' equal to zero and attempt to solve: Simplifying 5 + -5t + 8t2 = 0 Solving 5 + -5t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.625 + -0.625t + t2 = 0 Move the constant term to the right: Add '-0.625' to each side of the equation. 0.625 + -0.625t + -0.625 + t2 = 0 + -0.625 Reorder the terms: 0.625 + -0.625 + -0.625t + t2 = 0 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + -0.625t + t2 = 0 + -0.625 -0.625t + t2 = 0 + -0.625 Combine like terms: 0 + -0.625 = -0.625 -0.625t + t2 = -0.625 The t term is -0.625t. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625t + 0.09765625 + t2 = -0.625 + 0.09765625 Reorder the terms: 0.09765625 + -0.625t + t2 = -0.625 + 0.09765625 Combine like terms: -0.625 + 0.09765625 = -0.52734375 0.09765625 + -0.625t + t2 = -0.52734375 Factor a perfect square on the left side: (t + -0.3125)(t + -0.3125) = -0.52734375 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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