Solve Quadratic Equations by the Square Root Property
Solve the equation by the square root property.
-$$( 4 x + 3 ) ^ { 2 } = 7$$
A) $\left\{ \frac { - 3 - \sqrt { 7 } } { 4 } , \frac { - 3 + \sqrt { 7 } } { 4 } \right\}$
B) $\left\{ \frac { 3 - \sqrt { 7 } } { 4 } , \frac { 3 + \sqrt { 7 } } { 4 } \right\}$
C) $\left\{ \frac { \sqrt { 7 } - 3 } { 4 } , \frac { \sqrt { 7 } + 3 } { 4 } \right\}$
D) $\left\{ - \frac { 5 } { 2 } , 1 \right\}$

Question

Quizplus · Accepted Answer

To solve the equation using the square root property, first isolate the squared term: $(4x + 3)^2 = 7$. Taking the square root of both sides gives $4x + 3 = \pm\sqrt{7}$. Solving for $x$ yields $x = \frac{-3 \pm \sqrt{7}}{4}$, which matches choice A.

Solve Quadratic Equations by the Square Root Property Solve the Equation

Solve Quadratic Equations by the Square Root Property
Solve the Equation