Solve left(x+5right)^2-(x^2-4x+1)=6

$${ \left(x+5 \right) }^{ 2 } -( { x }^{ 2 } -4x+1) = 6$$

Solve for x

$$x = -\frac{9}{7} = -1\frac{2}{7} \approx -1.285714286$$

Steps for Solving Linear Equation

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

$$x^{2}+10x+25-\left(x^{2}-4x+1\right)=6$$

To find the opposite of x^{2}-4x+1, find the opposite of each term.

$$x^{2}+10x+25-x^{2}+4x-1=6$$

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

$$10x+25+4x-1=6$$

Combine 10x and 4x to get 14x.

$$14x+25-1=6$$

Subtract 1 from 25 to get 24.

$$14x+24=6$$

Subtract 24 from both sides.

$$14x=6-24$$

Subtract 24 from 6 to get -18.

$$14x=-18$$

Divide both sides by 14.

$$x=\frac{-18}{14}$$

Reduce the fraction \frac{-18}{14} to lowest terms by extracting and canceling out 2.

$$x=-\frac{9}{7}$$