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Simplifying 7(t + -3) + 7t = 7t(2t + 5) + -12 Reorder the terms: 7(-3 + t) + 7t = 7t(2t + 5) + -12 (-3 * 7 + t * 7) + 7t = 7t(2t + 5) + -12 (-21 + 7t) + 7t = 7t(2t + 5) + -12 Combine like terms: 7t + 7t = 14t -21 + 14t = 7t(2t + 5) + -12 Reorder the terms: -21 + 14t = 7t(5 + 2t) + -12 -21 + 14t = (5 * 7t + 2t * 7t) + -12 -21 + 14t = (35t + 14t2) + -12 Reorder the terms: -21 + 14t = -12 + 35t + 14t2 Solving -21 + 14t = -12 + 35t + 14t2 Solving for variable 't'. Reorder the terms: -21 + 12 + 14t + -35t + -14t2 = -12 + 35t + 14t2 + 12 + -35t + -14t2 Combine like terms: -21 + 12 = -9 -9 + 14t + -35t + -14t2 = -12 + 35t + 14t2 + 12 + -35t + -14t2 Combine like terms: 14t + -35t = -21t -9 + -21t + -14t2 = -12 + 35t + 14t2 + 12 + -35t + -14t2 Reorder the terms: -9 + -21t + -14t2 = -12 + 12 + 35t + -35t + 14t2 + -14t2 Combine like terms: -12 + 12 = 0 -9 + -21t + -14t2 = 0 + 35t + -35t + 14t2 + -14t2 -9 + -21t + -14t2 = 35t + -35t + 14t2 + -14t2 Combine like terms: 35t + -35t = 0 -9 + -21t + -14t2 = 0 + 14t2 + -14t2 -9 + -21t + -14t2 = 14t2 + -14t2 Combine like terms: 14t2 + -14t2 = 0 -9 + -21t + -14t2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(9 + 21t + 14t2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(9 + 21t + 14t2)' equal to zero and attempt to solve: Simplifying 9 + 21t + 14t2 = 0 Solving 9 + 21t + 14t2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. 0.6428571429 + 1.5t + t2 = 0 Move the constant term to the right: Add '-0.6428571429' to each side of the equation. 0.6428571429 + 1.5t + -0.6428571429 + t2 = 0 + -0.6428571429 Reorder the terms: 0.6428571429 + -0.6428571429 + 1.5t + t2 = 0 + -0.6428571429 Combine like terms: 0.6428571429 + -0.6428571429 = 0.0000000000 0.0000000000 + 1.5t + t2 = 0 + -0.6428571429 1.5t + t2 = 0 + -0.6428571429 Combine like terms: 0 + -0.6428571429 = -0.6428571429 1.5t + t2 = -0.6428571429 The t term is 1.5t. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5t + 0.5625 + t2 = -0.6428571429 + 0.5625 Reorder the terms: 0.5625 + 1.5t + t2 = -0.6428571429 + 0.5625 Combine like terms: -0.6428571429 + 0.5625 = -0.0803571429 0.5625 + 1.5t + t2 = -0.0803571429 Factor a perfect square on the left side: (t + 0.75)(t + 0.75) = -0.0803571429 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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