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Solve for $x$ . $\newline$ $\sqrt{8x} = \sqrt{1 + 9x}$ $\newline$ $x =$ _____

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Solve radical equations II

Full solution

Q. Solve for

x

.

\newline

\sqrt{8x} = \sqrt{1 + 9x}

\newline

x =

_____

Square Roots Elimination: First, we need to eliminate the square roots by squaring both sides of the equation. $\newline$ $(\sqrt{8x})^2 = (\sqrt{1 + 9x})^2$ $\newline$ This simplifies to: $\newline$ $8x = 1 + 9x$
Isolating Variable $x$ : Next, we need to isolate the variable $x$ . To do this, we will move all terms containing $x$ to one side of the equation. $8x - 9x = 1$ This simplifies to: $-x = 1$
Solving for x: To solve for x, we need to divide both sides of the equation by -1＂).\(\newline\$x = \frac{1}{-1}\)\(\newline\)This simplifies to:\(\newline\)\(x = -1\)

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