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Simplifying 2(t + 5) = -3t(2t + 2) Reorder the terms: 2(5 + t) = -3t(2t + 2) (5 * 2 + t * 2) = -3t(2t + 2) (10 + 2t) = -3t(2t + 2) Reorder the terms: 10 + 2t = -3t(2 + 2t) 10 + 2t = (2 * -3t + 2t * -3t) 10 + 2t = (-6t + -6t2) Solving 10 + 2t = -6t + -6t2 Solving for variable 't'. Combine like terms: 2t + 6t = 8t 10 + 8t + 6t2 = -6t + -6t2 + 6t + 6t2 Reorder the terms: 10 + 8t + 6t2 = -6t + 6t + -6t2 + 6t2 Combine like terms: -6t + 6t = 0 10 + 8t + 6t2 = 0 + -6t2 + 6t2 10 + 8t + 6t2 = -6t2 + 6t2 Combine like terms: -6t2 + 6t2 = 0 10 + 8t + 6t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 4t + 3t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + 4t + 3t2)' equal to zero and attempt to solve: Simplifying 5 + 4t + 3t2 = 0 Solving 5 + 4t + 3t2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.666666667 + 1.333333333t + t2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + 1.333333333t + -1.666666667 + t2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + 1.333333333t + t2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + 1.333333333t + t2 = 0 + -1.666666667 1.333333333t + t2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 1.333333333t + t2 = -1.666666667 The t term is 1.333333333t. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333t + 0.4444444442 + t2 = -1.666666667 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333t + t2 = -1.666666667 + 0.4444444442 Combine like terms: -1.666666667 + 0.4444444442 = -1.2222222228 0.4444444442 + 1.333333333t + t2 = -1.2222222228 Factor a perfect square on the left side: (t + 0.6666666665)(t + 0.6666666665) = -1.2222222228 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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