Solve 2.5left(4+xright)^2+7(5-x)(5+x)=295-4.5x^2

$$2.5 { \left(4+x \right) }^{ 2 } +7(5-x)(5+x)=295-4.5 { x }^{ 2 }$$

Solve for x

$$x=4$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(4+x\right)^{2}.

$$2.5\left(16+8x+x^{2}\right)+7\left(5-x\right)\left(5+x\right)=295-4.5x^{2}$$

Use the distributive property to multiply 2.5 by 16+8x+x^{2}.

$$40+20x+2.5x^{2}+7\left(5-x\right)\left(5+x\right)=295-4.5x^{2}$$

Use the distributive property to multiply 7 by 5-x.

$$40+20x+2.5x^{2}+\left(35-7x\right)\left(5+x\right)=295-4.5x^{2}$$

Use the distributive property to multiply 35-7x by 5+x and combine like terms.

$$40+20x+2.5x^{2}+175-7x^{2}=295-4.5x^{2}$$

Add 40 and 175 to get 215.

$$215+20x+2.5x^{2}-7x^{2}=295-4.5x^{2}$$

Combine 2.5x^{2} and -7x^{2} to get -4.5x^{2}.

$$215+20x-4.5x^{2}=295-4.5x^{2}$$

Add 4.5x^{2} to both sides.

$$215+20x-4.5x^{2}+4.5x^{2}=295$$

Combine -4.5x^{2} and 4.5x^{2} to get 0.

$$215+20x=295$$

Subtract 215 from both sides.

$$20x=295-215$$

Subtract 215 from 295 to get 80.

$$20x=80$$

Divide both sides by 20.

$$x=\frac{80}{20}$$

Divide 80 by 20 to get 4.

$$x=4$$