Solve 5x^2=4x^2+(3.6)^2

$$5 x ^ { 2 } = 4 x ^ { 2 } + ( 3.6 ) ^ { 2 }$$

Solve for x

$$x=3.6$$

$$x=-3.6$$

Steps Using Difference of Squares

Calculate 3.6 to the power of 2 and get 12.96.

$$5x^{2}=4x^{2}+12.96$$

Subtract 4x^{2} from both sides.

$$5x^{2}-4x^{2}=12.96$$

Combine 5x^{2} and -4x^{2} to get x^{2}.

$$x^{2}=12.96$$

Subtract 12.96 from both sides.

$$x^{2}-12.96=0$$

Consider x^{2}-12.96. Rewrite x^{2}-12.96 as x^{2}-\left(\frac{18}{5}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-\frac{18}{5}\right)\left(x+\frac{18}{5}\right)=0$$

To find equation solutions, solve x-\frac{18}{5}=0 and x+\frac{18}{5}=0.

$$x=\frac{18}{5} x=-3.6$$

Steps by Finding Square Root

Calculate 3.6 to the power of 2 and get 12.96.

$$5x^{2}=4x^{2}+12.96$$

Subtract 4x^{2} from both sides.

$$5x^{2}-4x^{2}=12.96$$

Combine 5x^{2} and -4x^{2} to get x^{2}.

$$x^{2}=12.96$$

Take the square root of both sides of the equation.

$$x=\frac{18}{5} x=-\frac{18}{5}$$

Steps Using the Quadratic Formula

Calculate 3.6 to the power of 2 and get 12.96.

$$5x^{2}=4x^{2}+12.96$$

Subtract 4x^{2} from both sides.

$$5x^{2}-4x^{2}=12.96$$

Combine 5x^{2} and -4x^{2} to get x^{2}.

$$x^{2}=12.96$$

Subtract 12.96 from both sides.

$$x^{2}-12.96=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -12.96 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-12.96\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-12.96\right)}}{2}$$

Multiply -4 times -12.96.

$$x=\frac{0±\sqrt{51.84}}{2}$$

Take the square root of 51.84.

$$x=\frac{0±\frac{36}{5}}{2}$$

Now solve the equation x=\frac{0±\frac{36}{5}}{2} when ± is plus.

$$x=\frac{18}{5}$$

Now solve the equation x=\frac{0±\frac{36}{5}}{2} when ± is minus.

$$x=-\frac{18}{5}$$

The equation is now solved.

$$x=\frac{18}{5} x=-\frac{18}{5}$$