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Simplifying t(t + 8) + 5(t2 + 6) = 0 Reorder the terms: t(8 + t) + 5(t2 + 6) = 0 (8 * t + t * t) + 5(t2 + 6) = 0 (8t + t2) + 5(t2 + 6) = 0 Reorder the terms: 8t + t2 + 5(6 + t2) = 0 8t + t2 + (6 * 5 + t2 * 5) = 0 8t + t2 + (30 + 5t2) = 0 Reorder the terms: 30 + 8t + t2 + 5t2 = 0 Combine like terms: t2 + 5t2 = 6t2 30 + 8t + 6t2 = 0 Solving 30 + 8t + 6t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(15 + 4t + 3t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(15 + 4t + 3t2)' equal to zero and attempt to solve: Simplifying 15 + 4t + 3t2 = 0 Solving 15 + 4t + 3t2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 5 + 1.333333333t + t2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + 1.333333333t + -5 + t2 = 0 + -5 Reorder the terms: 5 + -5 + 1.333333333t + t2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 1.333333333t + t2 = 0 + -5 1.333333333t + t2 = 0 + -5 Combine like terms: 0 + -5 = -5 1.333333333t + t2 = -5 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 = -5 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333t + t2 = -5 + 0.4444444442 Combine like terms: -5 + 0.4444444442 = -4.5555555558 0.4444444442 + 1.333333333t + t2 = -4.5555555558 Factor a perfect square on the left side: (t + 0.6666666665)(t + 0.6666666665) = -4.5555555558 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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