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Simplifying 22 = 16t2 + 28t + 40 Reorder the terms: 22 = 40 + 28t + 16t2 Solving 22 = 40 + 28t + 16t2 Solving for variable 't'. Combine like terms: 22 + -40 = -18 -18 + -28t + -16t2 = 40 + 28t + 16t2 + -40 + -28t + -16t2 Reorder the terms: -18 + -28t + -16t2 = 40 + -40 + 28t + -28t + 16t2 + -16t2 Combine like terms: 40 + -40 = 0 -18 + -28t + -16t2 = 0 + 28t + -28t + 16t2 + -16t2 -18 + -28t + -16t2 = 28t + -28t + 16t2 + -16t2 Combine like terms: 28t + -28t = 0 -18 + -28t + -16t2 = 0 + 16t2 + -16t2 -18 + -28t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -18 + -28t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(9 + 14t + 8t2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(9 + 14t + 8t2)' equal to zero and attempt to solve: Simplifying 9 + 14t + 8t2 = 0 Solving 9 + 14t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.125 + 1.75t + t2 = 0 Move the constant term to the right: Add '-1.125' to each side of the equation. 1.125 + 1.75t + -1.125 + t2 = 0 + -1.125 Reorder the terms: 1.125 + -1.125 + 1.75t + t2 = 0 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + 1.75t + t2 = 0 + -1.125 1.75t + t2 = 0 + -1.125 Combine like terms: 0 + -1.125 = -1.125 1.75t + t2 = -1.125 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 = -1.125 + 0.765625 Reorder the terms: 0.765625 + 1.75t + t2 = -1.125 + 0.765625 Combine like terms: -1.125 + 0.765625 = -0.359375 0.765625 + 1.75t + t2 = -0.359375 Factor a perfect square on the left side: (t + 0.875)(t + 0.875) = -0.359375 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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