Solve {left(8.2+5.3/2right)}^2*9=x^2

$${ \left( \frac{ 8.2+5.3 }{ 2 } \right) }^{ 2 } \times 9= { x }^{ 2 }$$

Solve for x

$$x=20.25$$

$$x=-20.25$$

Steps Using Difference of Squares

Add 8.2 and 5.3 to get 13.5.

$$\left(\frac{13.5}{2}\right)^{2}\times 9=x^{2}$$

Expand \frac{13.5}{2} by multiplying both numerator and the denominator by 10.

$$\left(\frac{135}{20}\right)^{2}\times 9=x^{2}$$

Reduce the fraction \frac{135}{20} to lowest terms by extracting and canceling out 5.

$$\left(\frac{27}{4}\right)^{2}\times 9=x^{2}$$

Calculate \frac{27}{4} to the power of 2 and get \frac{729}{16}.

$$\frac{729}{16}\times 9=x^{2}$$

Multiply \frac{729}{16} and 9 to get \frac{6561}{16}.

$$\frac{6561}{16}=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=\frac{6561}{16}$$

Subtract \frac{6561}{16} from both sides.

$$x^{2}-\frac{6561}{16}=0$$

Multiply both sides by 16.

$$16x^{2}-6561=0$$

Consider 16x^{2}-6561. Rewrite 16x^{2}-6561 as \left(4x\right)^{2}-81^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(4x-81\right)\left(4x+81\right)=0$$

To find equation solutions, solve 4x-81=0 and 4x+81=0.

$$x=\frac{81}{4} x=-\frac{81}{4}$$

Steps by Finding Square Root

Add 8.2 and 5.3 to get 13.5.

$$\left(\frac{13.5}{2}\right)^{2}\times 9=x^{2}$$

Expand \frac{13.5}{2} by multiplying both numerator and the denominator by 10.

$$\left(\frac{135}{20}\right)^{2}\times 9=x^{2}$$

Reduce the fraction \frac{135}{20} to lowest terms by extracting and canceling out 5.

$$\left(\frac{27}{4}\right)^{2}\times 9=x^{2}$$

Calculate \frac{27}{4} to the power of 2 and get \frac{729}{16}.

$$\frac{729}{16}\times 9=x^{2}$$

Multiply \frac{729}{16} and 9 to get \frac{6561}{16}.

$$\frac{6561}{16}=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=\frac{6561}{16}$$

Take the square root of both sides of the equation.

$$x=\frac{81}{4} x=-\frac{81}{4}$$

Steps Using the Quadratic Formula

Add 8.2 and 5.3 to get 13.5.

$$\left(\frac{13.5}{2}\right)^{2}\times 9=x^{2}$$

Expand \frac{13.5}{2} by multiplying both numerator and the denominator by 10.

$$\left(\frac{135}{20}\right)^{2}\times 9=x^{2}$$

Reduce the fraction \frac{135}{20} to lowest terms by extracting and canceling out 5.

$$\left(\frac{27}{4}\right)^{2}\times 9=x^{2}$$

Calculate \frac{27}{4} to the power of 2 and get \frac{729}{16}.

$$\frac{729}{16}\times 9=x^{2}$$

Multiply \frac{729}{16} and 9 to get \frac{6561}{16}.

$$\frac{6561}{16}=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=\frac{6561}{16}$$

Subtract \frac{6561}{16} from both sides.

$$x^{2}-\frac{6561}{16}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{6561}{16} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{6561}{16}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{6561}{16}\right)}}{2}$$

Multiply -4 times -\frac{6561}{16}.

$$x=\frac{0±\sqrt{\frac{6561}{4}}}{2}$$

Take the square root of \frac{6561}{4}.

$$x=\frac{0±\frac{81}{2}}{2}$$

Now solve the equation x=\frac{0±\frac{81}{2}}{2} when ± is plus.

$$x=\frac{81}{4}$$

Now solve the equation x=\frac{0±\frac{81}{2}}{2} when ± is minus.

$$x=-\frac{81}{4}$$

The equation is now solved.

$$x=\frac{81}{4} x=-\frac{81}{4}$$