Solve x^2+(x+1)^2=(2x-1)(x+3)

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

Solve for x

$$x = \frac{4}{3} = 1\frac{1}{3} \approx 1.333333333$$

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}.

$$x^{2}+x^{2}+2x+1=\left(2x-1\right)\left(x+3\right)$$

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

$$2x^{2}+2x+1=\left(2x-1\right)\left(x+3\right)$$

Use the distributive property to multiply 2x-1 by x+3 and combine like terms.

$$2x^{2}+2x+1=2x^{2}+5x-3$$

Subtract 2x^{2} from both sides.

$$2x^{2}+2x+1-2x^{2}=5x-3$$

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

$$2x+1=5x-3$$

Subtract 5x from both sides.

$$2x+1-5x=-3$$

Combine 2x and -5x to get -3x.

$$-3x+1=-3$$

Subtract 1 from both sides.

$$-3x=-3-1$$

Subtract 1 from -3 to get -4.

$$-3x=-4$$

Divide both sides by -3.

$$x=\frac{-4}{-3}$$

Fraction \frac{-4}{-3} can be simplified to \frac{4}{3} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{4}{3}$$