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Simplifying -2(t + 6) = 5t(t + 1) Reorder the terms: -2(6 + t) = 5t(t + 1) (6 * -2 + t * -2) = 5t(t + 1) (-12 + -2t) = 5t(t + 1) Reorder the terms: -12 + -2t = 5t(1 + t) -12 + -2t = (1 * 5t + t * 5t) -12 + -2t = (5t + 5t2) Solving -12 + -2t = 5t + 5t2 Solving for variable 't'. Combine like terms: -2t + -5t = -7t -12 + -7t + -5t2 = 5t + 5t2 + -5t + -5t2 Reorder the terms: -12 + -7t + -5t2 = 5t + -5t + 5t2 + -5t2 Combine like terms: 5t + -5t = 0 -12 + -7t + -5t2 = 0 + 5t2 + -5t2 -12 + -7t + -5t2 = 5t2 + -5t2 Combine like terms: 5t2 + -5t2 = 0 -12 + -7t + -5t2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(12 + 7t + 5t2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(12 + 7t + 5t2)' equal to zero and attempt to solve: Simplifying 12 + 7t + 5t2 = 0 Solving 12 + 7t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.4 + 1.4t + t2 = 0 Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + 1.4t + -2.4 + t2 = 0 + -2.4 Reorder the terms: 2.4 + -2.4 + 1.4t + t2 = 0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + 1.4t + t2 = 0 + -2.4 1.4t + t2 = 0 + -2.4 Combine like terms: 0 + -2.4 = -2.4 1.4t + t2 = -2.4 The t term is 1.4t. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4t + 0.49 + t2 = -2.4 + 0.49 Reorder the terms: 0.49 + 1.4t + t2 = -2.4 + 0.49 Combine like terms: -2.4 + 0.49 = -1.91 0.49 + 1.4t + t2 = -1.91 Factor a perfect square on the left side: (t + 0.7)(t + 0.7) = -1.91 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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