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Simplifying -16t2 + 28t = 14 Reorder the terms: 28t + -16t2 = 14 Solving 28t + -16t2 = 14 Solving for variable 't'. Reorder the terms: -14 + 28t + -16t2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + 28t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + 14t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + 14t + -8t2)' equal to zero and attempt to solve: Simplifying -7 + 14t + -8t2 = 0 Solving -7 + 14t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 0.875 + -1.75t + t2 = 0 Move the constant term to the right: Add '-0.875' to each side of the equation. 0.875 + -1.75t + -0.875 + t2 = 0 + -0.875 Reorder the terms: 0.875 + -0.875 + -1.75t + t2 = 0 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + -1.75t + t2 = 0 + -0.875 -1.75t + t2 = 0 + -0.875 Combine like terms: 0 + -0.875 = -0.875 -1.75t + t2 = -0.875 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 = -0.875 + 0.765625 Reorder the terms: 0.765625 + -1.75t + t2 = -0.875 + 0.765625 Combine like terms: -0.875 + 0.765625 = -0.109375 0.765625 + -1.75t + t2 = -0.109375 Factor a perfect square on the left side: (t + -0.875)(t + -0.875) = -0.109375 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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