Question

How do I do this lol

Answer 1

Assignment: $\bold{Solve \ Equation: \ x=\sqrt{13x-42}}$

<><><><><><><>

Answer: $\boxed{\bold{x=7,\:x=6}}$

<><><><><><><>

Explanation: $\downarrow\downarrow\downarrow$

<><><><><><><>

[ Step One ] Square Both Sides

$\bold{x^2=\left(\sqrt{13x-42}\right)^2}$

[ Step Two ] Expand $\bold{\left(\sqrt{13x-42}\right)^2}$

$\bold{13x-42}$

[ Step Three ] Rewrite Equation

$\bold{x^2=13x-42}$

[ Step Four ] Solve $\bold{x^2=13x-42}$

$\bold{x=7,\:x=6}$

<><><><><><><>

$\bold{\rightarrow Mordancy \leftarrow}$

Answer 2

Answer:

x = 6, x = 7

Step-by-step explanation:

Given

x = $\sqrt{13x-42}$ ← square both sides

x² = 13x - 42 ← subtract 13x - 42 from both sides

x² - 13x + 42 = 0 ← in standard form

(x - 6)(x - 7) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x - 7 = 0 ⇒ x = 7

As a check substitute these values into the right side of the equation and if equal to the left side then they are the solutions

x = 6 : $\sqrt{78-42}$ = $\sqrt{36}$ = 6 ← solution

x = 7 : $\sqrt{91-42}$ = $\sqrt{49}$ = 7 ← solution