Solve left(x+1right)^2+left(x-6right)^2=2x^2

$${ \left(x+1 \right) }^{ 2 } + { \left(x-6 \right) }^{ 2 } =2 { x }^{ 2 }$$

Solve for x

$$x = \frac{37}{10} = 3\frac{7}{10} = 3.7$$

Steps for Solving Linear Equation

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

$$x^{2}+2x+1+\left(x-6\right)^{2}=2x^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-6\right)^{2}.

$$x^{2}+2x+1+x^{2}-12x+36=2x^{2}$$

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

$$2x^{2}+2x+1-12x+36=2x^{2}$$

Combine 2x and -12x to get -10x.

$$2x^{2}-10x+1+36=2x^{2}$$

Add 1 and 36 to get 37.

$$2x^{2}-10x+37=2x^{2}$$

Subtract 2x^{2} from both sides.

$$2x^{2}-10x+37-2x^{2}=0$$

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

$$-10x+37=0$$

Subtract 37 from both sides. Anything subtracted from zero gives its negation.

$$-10x=-37$$

Divide both sides by -10.

$$x=\frac{-37}{-10}$$

Fraction \frac{-37}{-10} can be simplified to \frac{37}{10} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{37}{10}$$