Solve (5x+2)^2=(3+3x)^2+(1+4x)^2

$$( 5 x + 2 ) ^ { 2 } = ( 3 + 3 x ) ^ { 2 } + ( 1 + 4 x ) ^ { 2 }$$

Solve for x

$$x=-1$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(5x+2\right)^{2}.

$$25x^{2}+20x+4=\left(3+3x\right)^{2}+\left(1+4x\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3+3x\right)^{2}.

$$25x^{2}+20x+4=9+18x+9x^{2}+\left(1+4x\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(1+4x\right)^{2}.

$$25x^{2}+20x+4=9+18x+9x^{2}+1+8x+16x^{2}$$

Add 9 and 1 to get 10.

$$25x^{2}+20x+4=10+18x+9x^{2}+8x+16x^{2}$$

Combine 18x and 8x to get 26x.

$$25x^{2}+20x+4=10+26x+9x^{2}+16x^{2}$$

Combine 9x^{2} and 16x^{2} to get 25x^{2}.

$$25x^{2}+20x+4=10+26x+25x^{2}$$

Subtract 26x from both sides.

$$25x^{2}+20x+4-26x=10+25x^{2}$$

Combine 20x and -26x to get -6x.

$$25x^{2}-6x+4=10+25x^{2}$$

Subtract 25x^{2} from both sides.

$$25x^{2}-6x+4-25x^{2}=10$$

Combine 25x^{2} and -25x^{2} to get 0.

$$-6x+4=10$$

Subtract 4 from both sides.

$$-6x=10-4$$

Subtract 4 from 10 to get 6.

$$-6x=6$$

Divide both sides by -6.

$$x=\frac{6}{-6}$$

Divide 6 by -6 to get -1.

$$x=-1$$