Write Equation: Write down the given equation. The given equation is (2/3)x^2 = 4.8^2. We need to find the value of x.Calculate Square: Calculate the square of 4.8. 4.8^2 = 4.8 * 4.8 = 23.04. So, the equation now is (2/3)x^2 = 23.04.Multiply to Isolate: Multiply both sides of the equation by 3/2 to isolate x^2. (3/2) * (2/3)x^2 = 23.04 * (3/2). This simplifies to x^2 = 23.04 * (3/2).Calculate Right Side: Calculate the right side of the equation. x^2 = 23.04 * (3/2) = 23.04 * 1.5 = 34.56. So, the equation now is x^2 = 34.56.Take Square Root: Take the square root of both sides to solve for x. √(x^2) = √(34.56). This simplifies to x = √(34.56).Calculate Final Value: Calculate the square root of 34.56. x = √(34.56) ≈ 5.878. So, the value of x is approximately 5.878.

Algebra 1

Powers with decimal and fractional bases

Full solution

\frac{2}{3}x^2=4.8^2

Write Equation: Write down the given equation. $\newline$ The given equation is $(\frac{2}{3})x^2 = 4.8^2$ . We need to find the value of $x$ .
Calculate Square: Calculate the square of $4.8$ . $\newline$ $4.8^2 = 4.8 \times 4.8 = 23.04$ . $\newline$ So, the equation now is $(\frac{2}{3})x^2 = 23.04$ .
Multiply to Isolate: Multiply both sides of the equation by $\frac{3}{2}$ to isolate $x^2$ . $\newline$ $(\frac{3}{2}) \cdot (\frac{2}{3})x^2 = 23.04 \cdot (\frac{3}{2})$ . $\newline$ This simplifies to $x^2 = 23.04 \cdot (\frac{3}{2})$ .
Calculate Right Side: Calculate the right side of the equation. $\newline$ $x^2 = 23.04 \times \left(\frac{3}{2}\right) = 23.04 \times 1.5 = 34.56.$ $\newline$ So, the equation now is $x^2 = 34.56.$
Take Square Root: Take the square root of both sides to solve for $x$ . $\sqrt{x^2} = \sqrt{34.56}$ . This simplifies to $x = \sqrt{34.56}$ .
Calculate Final Value: Calculate the square root of $34.56$ . $x = \sqrt{34.56} \approx 5.878$ .So, the value of $x$ is approximately $5.878$ .