Solve (x+2)^2=x*(x+4,9)+9

$$( x + 2 ) ^ { 2 } = x \cdot ( x + 4,9 ) + 9$$

Solve for x

$$x=-\frac{50}{9}\approx -5,555555556$$

Steps for Solving Linear Equation

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

$$x^{2}+4x+4=x\left(x+4,9\right)+9$$

Use the distributive property to multiply x by x+4,9.

$$x^{2}+4x+4=x^{2}+4,9x+9$$

Subtract x^{2} from both sides.

$$x^{2}+4x+4-x^{2}=4,9x+9$$

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

$$4x+4=4,9x+9$$

Subtract 4,9x from both sides.

$$4x+4-4,9x=9$$

Combine 4x and -4,9x to get -0,9x.

$$-0,9x+4=9$$

Subtract 4 from both sides.

$$-0,9x=9-4$$

Subtract 4 from 9 to get 5.

$$-0,9x=5$$

Divide both sides by -0,9.

$$x=\frac{5}{-0,9}$$

Expand \frac{5}{-0,9} by multiplying both numerator and the denominator by 10.

$$x=\frac{50}{-9}$$

Fraction \frac{50}{-9} can be rewritten as -\frac{50}{9} by extracting the negative sign.

$$x=-\frac{50}{9}$$