Solve the equation using the quadratic formula.
-$$( 2 x - 1 ) ( x + 1 ) = 3$$
A) $\left\{ \frac { - 1 \pm \sqrt { 33 } } { 4 } \right\}$
B) $\left\{ \frac { 1 \pm \sqrt { 33 } } { 4 } \right\}$
C) $\left\{ \frac { - 1 \pm \sqrt { 57 } } { 2 } \right\}$
D) $\left\{ \frac { 1 \pm \sqrt { 33 } } { 2 } \right\}$

Question

Quizplus · Accepted Answer

First, expand the equation: $2x^2 + 2x - x - 1 = 3$, simplifying to $2x^2 + x - 4 = 0$. Using the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ with $a = 2$, $b = 1$, and $c = -4$, we get $x = \frac{-1 \pm \sqrt{1 + 32}}{4}$, which simplifies to $x = \frac{-1 \pm \sqrt{33}}{4}$.

Solve the Equation Using the Quadratic Formula (2x−1)(x+1)=3( 2 x - 1 ) ( x + 1 ) = 3(2x−1)(x+1)=3

Solve the Equation Using the Quadratic Formula $( 2 x - 1 ) ( x + 1 ) = 3$