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antiseptic1488 [7]
3 years ago
11

How do I do this lol

Mathematics
2 answers:
Veseljchak [2.6K]3 years ago
7 0

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}

umka2103 [35]3 years ago
7 0

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

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