Solve sqrt{5x+3}=3sqrt{x}?

$$\sqrt { 5 x + 3 } = 3 \sqrt { x } ?$$

Solve for x

$$x=\frac{3}{4}=0.75$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{5x+3}\right)^{2}=\left(3\sqrt{x}\right)^{2}$$

Calculate \sqrt{5x+3} to the power of 2 and get 5x+3.

$$5x+3=\left(3\sqrt{x}\right)^{2}$$

Expand \left(3\sqrt{x}\right)^{2}.

$$5x+3=3^{2}\left(\sqrt{x}\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$5x+3=9\left(\sqrt{x}\right)^{2}$$

Calculate \sqrt{x} to the power of 2 and get x.

$$5x+3=9x$$

Subtract 9x from both sides.

$$5x+3-9x=0$$

Combine 5x and -9x to get -4x.

$$-4x+3=0$$

Subtract 3 from both sides. Anything subtracted from zero gives its negation.

$$-4x=-3$$

Divide both sides by -4.

$$x=\frac{-3}{-4}$$

Fraction \frac{-3}{-4} can be simplified to \frac{3}{4} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{3}{4}$$

Substitute \frac{3}{4} for x in the equation \sqrt{5x+3}=3\sqrt{x}.

$$\sqrt{5\times \frac{3}{4}+3}=3\sqrt{\frac{3}{4}}$$

Simplify. The value x=\frac{3}{4} satisfies the equation.

$$\frac{3}{2}\times 3^{\frac{1}{2}}=\frac{3}{2}\times 3^{\frac{1}{2}}$$

Equation \sqrt{5x+3}=3\sqrt{x} has a unique solution.

$$x=\frac{3}{4}$$