Solve left(3xright)^2=6.93^2

$${ \left(3x \right) }^{ 2 } = { 6.93 }^{ 2 }$$

Solve for x

$$x=2.31$$

$$x=-2.31$$

Steps Using Difference of Squares

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

$$3^{2}x^{2}=6.93^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9x^{2}=6.93^{2}$$

Calculate 6.93 to the power of 2 and get 48.0249.

$$9x^{2}=48.0249$$

Subtract 48.0249 from both sides.

$$9x^{2}-48.0249=0$$

Consider 9x^{2}-48.0249. Rewrite 9x^{2}-48.0249 as \left(3x\right)^{2}-\left(\frac{693}{100}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(3x-\frac{693}{100}\right)\left(3x+\frac{693}{100}\right)=0$$

To find equation solutions, solve 3x-\frac{693}{100}=0 and 3x+\frac{693}{100}=0.

$$x=\frac{231}{100} x=-\frac{231}{100}$$

Steps by Finding Square Root

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

$$3^{2}x^{2}=6.93^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9x^{2}=6.93^{2}$$

Calculate 6.93 to the power of 2 and get 48.0249.

$$9x^{2}=48.0249$$

Divide both sides by 9.

$$x^{2}=\frac{48.0249}{9}$$

Expand \frac{48.0249}{9} by multiplying both numerator and the denominator by 10000.

$$x^{2}=\frac{480249}{90000}$$

Reduce the fraction \frac{480249}{90000} to lowest terms by extracting and canceling out 9.

$$x^{2}=\frac{53361}{10000}$$

Take the square root of both sides of the equation.

$$x=\frac{231}{100} x=-\frac{231}{100}$$

Steps Using the Quadratic Formula

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

$$3^{2}x^{2}=6.93^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9x^{2}=6.93^{2}$$

Calculate 6.93 to the power of 2 and get 48.0249.

$$9x^{2}=48.0249$$

Subtract 48.0249 from both sides.

$$9x^{2}-48.0249=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 9 for a, 0 for b, and -48.0249 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 9\left(-48.0249\right)}}{2\times 9}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 9\left(-48.0249\right)}}{2\times 9}$$

Multiply -4 times 9.

$$x=\frac{0±\sqrt{-36\left(-48.0249\right)}}{2\times 9}$$

Multiply -36 times -48.0249.

$$x=\frac{0±\sqrt{1728.8964}}{2\times 9}$$

Take the square root of 1728.8964.

$$x=\frac{0±\frac{2079}{50}}{2\times 9}$$

Multiply 2 times 9.

$$x=\frac{0±\frac{2079}{50}}{18}$$

Now solve the equation x=\frac{0±\frac{2079}{50}}{18} when ± is plus.

$$x=\frac{231}{100}$$

Now solve the equation x=\frac{0±\frac{2079}{50}}{18} when ± is minus.

$$x=-\frac{231}{100}$$

The equation is now solved.

$$x=\frac{231}{100} x=-\frac{231}{100}$$