How to solve sqrt(x) = 6/4 * x

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve sqrt(x) = 6/4 * x | Equatix

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Question

$$\sqrt{x}=\frac{6}{4}x$$

Solve for x

$x=0$
$x=\frac{4}{9}\approx 0.444444444$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{x}\right)^{2}=\left(\frac{6}{4}x\right)^{2}$$

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

$$x=\left(\frac{6}{4}x\right)^{2}$$

Reduce the fraction $\frac{6}{4}$ to lowest terms by extracting and canceling out $2$.

$$x=\left(\frac{3}{2}x\right)^{2}$$

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

$$x=\left(\frac{3}{2}\right)^{2}x^{2}$$

Calculate $\frac{3}{2}$ to the power of $2$ and get $\frac{9}{4}$.

$$x=\frac{9}{4}x^{2}$$

Subtract $\frac{9}{4}x^{2}$ from both sides.

$$x-\frac{9}{4}x^{2}=0$$

Factor out $x$.

$$x\left(1-\frac{9}{4}x\right)=0$$

To find equation solutions, solve $x=0$ and $1-\frac{9x}{4}=0$.

$$x=0$$ $$x=\frac{4}{9}$$

Substitute $0$ for $x$ in the equation $\sqrt{x}=\frac{6}{4}x$.

$$\sqrt{0}=\frac{6}{4}\times 0$$

Simplify. The value $x=0$ satisfies the equation.

$$0=0$$

Substitute $\frac{4}{9}$ for $x$ in the equation $\sqrt{x}=\frac{6}{4}x$.

$$\sqrt{\frac{4}{9}}=\frac{6}{4}\times \frac{4}{9}$$

Simplify. The value $x=\frac{4}{9}$ satisfies the equation.

$$\frac{2}{3}=\frac{2}{3}$$

List all solutions of $\sqrt{x}=\frac{3}{2}x$.