Solve x^2+(16)^2+(20-x)^2+(22)^2

$$x ^ { 2 } + ( 16 ) ^ { 2 } + ( 20 - x ) ^ { 2 } + ( 22 ) ^ { 2 }$$

Evaluate

$$2\left(x^{2}-20x+570\right)$$

Solution Steps

Calculate 16 to the power of 2 and get 256.

$$x^{2}+256+\left(20-x\right)^{2}+22^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(20-x\right)^{2}.

$$x^{2}+256+400-40x+x^{2}+22^{2}$$

Add 256 and 400 to get 656.

$$x^{2}+656-40x+x^{2}+22^{2}$$

Combine x^{2} and x^{2} to get 2x^{2}.

$$2x^{2}+656-40x+22^{2}$$

Calculate 22 to the power of 2 and get 484.

$$2x^{2}+656-40x+484$$

Add 656 and 484 to get 1140.

$$2x^{2}+1140-40x$$

Expand

$$2x^{2}-40x+1140$$

Solution Steps

Calculate 16 to the power of 2 and get 256.

$$x^{2}+256+\left(20-x\right)^{2}+22^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(20-x\right)^{2}.

$$x^{2}+256+400-40x+x^{2}+22^{2}$$

Add 256 and 400 to get 656.

$$x^{2}+656-40x+x^{2}+22^{2}$$

Combine x^{2} and x^{2} to get 2x^{2}.

$$2x^{2}+656-40x+22^{2}$$

Calculate 22 to the power of 2 and get 484.

$$2x^{2}+656-40x+484$$

Add 656 and 484 to get 1140.

$$2x^{2}+1140-40x$$