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Simplifying -16t2 + 28t + -32 = 0 Reorder the terms: -32 + 28t + -16t2 = 0 Solving -32 + 28t + -16t2 = 0 Solving for variable 't'. 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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