Solve the equation by factoring.
-$$30 x ^ { 2 } + 51 x + 18 = 0$$
A) $x = - \frac { 6 } { 5 }$ or $x = - \frac { 1 } { 2 }$
B) $x = \frac { 6 } { 5 }$ or $x = \frac { 1 } { 2 }$
C) $x = \frac { 5 } { 6 }$ or $x = 2$
D) $x = - \frac { 5 } { 6 }$ or $x = - \frac { 1 } { 2 }$

Question

Quizplus · Accepted Answer

To solve the equation $30x^2 + 51x + 18 = 0$ by factoring, we look for two numbers that multiply to $30 \times 18 = 540$ and add to 51. These numbers are 30 and 18, which can be used to rewrite the middle term: $30x^2 + 30x + 21x + 18 = 0$. Factoring by grouping, we get $6x(5x + 5) + 3(5x + 5) = 0$, simplifying to $(6x + 3)(5x + 5) = 0$. Solving for $x$ gives $x = -\frac{1}{2}$ and $x = -\frac{6}{5}$.

Solve the Equation by Factoring 30x2+51x+18=030 x ^ { 2 } + 51 x + 18 = 030x2+51x+18=0

Solve the Equation by Factoring $30 x ^ { 2 } + 51 x + 18 = 0$