Solve x^2=27(27+21)

$${ x }^{ 2 } =27(27+21)$$

Solve for x

$$x=36$$

$$x=-36$$

Steps Using Difference of Squares

Add 27 and 21 to get 48.

$$x^{2}=27\times 48$$

Multiply 27 and 48 to get 1296.

$$x^{2}=1296$$

Subtract 1296 from both sides.

$$x^{2}-1296=0$$

Consider x^{2}-1296. Rewrite x^{2}-1296 as x^{2}-36^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-36\right)\left(x+36\right)=0$$

To find equation solutions, solve x-36=0 and x+36=0.

$$x=36 x=-36$$

Steps by Finding Square Root

Add 27 and 21 to get 48.

$$x^{2}=27\times 48$$

Multiply 27 and 48 to get 1296.

$$x^{2}=1296$$

Take the square root of both sides of the equation.

$$x=36 x=-36$$

Steps Using the Quadratic Formula

Add 27 and 21 to get 48.

$$x^{2}=27\times 48$$

Multiply 27 and 48 to get 1296.

$$x^{2}=1296$$

Subtract 1296 from both sides.

$$x^{2}-1296=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -1296 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1296\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1296\right)}}{2}$$

Multiply -4 times -1296.

$$x=\frac{0±\sqrt{5184}}{2}$$

Take the square root of 5184.

$$x=\frac{0±72}{2}$$

Now solve the equation x=\frac{0±72}{2} when ± is plus. Divide 72 by 2.

$$x=36$$

Now solve the equation x=\frac{0±72}{2} when ± is minus. Divide -72 by 2.

$$x=-36$$

The equation is now solved.

$$x=36 x=-36$$