Solve Radical Equations
Solve the radical equation, and check all proposed solutions.
-$$\sqrt { 8 x + 20 } = x$$
A) $\{ 10 \}$
B) $\{ - 2,10 \}$
C) $\left\{ - \frac { 20 } { 7 } \right\}$
D) $\varnothing$

Question

Quizplus · Accepted Answer

To solve the equation $\sqrt{8x + 20} = x$, we first square both sides to eliminate the square root, resulting in $8x + 20 = x^2$. Rearranging gives $x^2 - 8x - 20 = 0$. Factoring or using the quadratic formula, we find that the solutions are $x = -2$ and $x = 10$. However, when we substitute $x = -2$ back into the original equation, it does not satisfy the equation because the square root of a number cannot be negative. Therefore, the only solution that works is $x = 10$.

Solve Radical Equations Solve the Radical Equation, and Check All 8x+20=x\sqrt { 8 x + 20 } = x8x+20​=x

Solve Radical Equations
Solve the Radical Equation, and Check All $\sqrt { 8 x + 20 } = x$