Expert answers to "To calculate: Thesolution set of the equation 6t(21+1)=5−5t."

High School
Algebra
Pre-Algebra
Equations, expressions, and inequalitie

korporasidn

Answered question

2021-11-12

To calculate: Thesolution set of the equation

6 t (21 + 1) = 5 - 5 t

Answer & Explanation

Salvador Fry

Beginner2021-11-13Added 12 answers

Consider the provided equation,
$6 t (2 t + 1) = 5 - 5 t$
Now, apply the distributive property and solve,
$6 t (2 t + 1) = 5 - 5 t$
$12 t^{2} + 6 t = 5 - 5 t$
$12 t^{2} + 6 t + 5 = 5 t$
$12 t^{2} + 11 t = 5$
Now, solve the above equation by completing the square,
$12 t^{2} + 11 t = 5$
$t^{2} + \frac{11}{12} t = \frac{5}{12}$
$t^{2} + \frac{11}{12} t + {(\frac{11}{24})}^{2} = \frac{5}{12} + {(\frac{11}{24})}^{2}$
${(t + \frac{11}{24})}^{2} = \frac{5}{12} + \frac{121}{576}$
Further simplify the above equation,
${(t + \frac{11}{24})}^{2} = \frac{5}{12} + \frac{121}{576}$
${(t + \frac{11}{24})}^{2} = \frac{240}{576} + \frac{121}{576}$
${(t + \frac{11}{24})}^{2} = \frac{361}{576}$
Now, apply the square root property in the above equation;
${(t + \frac{11}{24})}^{2} = \frac{361}{576}$
$t + \frac{11}{24} = \pm \sqrt{\frac{361}{576}}$
$t + \frac{11}{24} = \pm \frac{19}{24}$
$t = - \frac{11}{24} \pm \frac{19}{24}$
Therefore $t = - \frac{11}{24} + \frac{19}{24} and t = - \frac{11}{24} - \frac{19}{24}$
That is, $t = \frac{1}{3} and t = \frac{5}{4}$
Check:
Now, substitute value of $t = \frac{1}{3}$ in the provided equation $6 t (2 t + 1) = 5 - 5 t$ .
$6 t (2 t + 1) 5 - 5 t$
$6 (\frac{1}{3}) (2 x \frac{1}{3} + 1) 5 - 5 (\frac{1}{3})$
$2 (\frac{2}{3} + 1) 5 - \frac{5}{3}$

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