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Simplifying 32 = -16t2 + 28t + 0 Reorder the terms: 32 = 0 + 28t + -16t2 Remove the zero: 32 = 28t + -16t2 Solving 32 = 28t + -16t2 Solving for variable 't'. Reorder the terms: 32 + -28t + 16t2 = 28t + -28t + -16t2 + 16t2 Combine like terms: 28t + -28t = 0 32 + -28t + 16t2 = 0 + -16t2 + 16t2 32 + -28t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 32 + -28t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(8 + -7t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(8 + -7t + 4t2)' equal to zero and attempt to solve: Simplifying 8 + -7t + 4t2 = 0 Solving 8 + -7t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2 + -1.75t + t2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -1.75t + -2 + t2 = 0 + -2 Reorder the terms: 2 + -2 + -1.75t + t2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1.75t + t2 = 0 + -2 -1.75t + t2 = 0 + -2 Combine like terms: 0 + -2 = -2 -1.75t + t2 = -2 The t term is -1.75t. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75t + 0.765625 + t2 = -2 + 0.765625 Reorder the terms: 0.765625 + -1.75t + t2 = -2 + 0.765625 Combine like terms: -2 + 0.765625 = -1.234375 0.765625 + -1.75t + t2 = -1.234375 Factor a perfect square on the left side: (t + -0.875)(t + -0.875) = -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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