Solve (x+2)^2=x*(x+4.9)+9

$$( x + 2 ) ^ { 2 } = x \cdot ( x + 4.9 ) + 9$$

Solve for x

$$x = -\frac{50}{9} = -5\frac{5}{9} \approx -5.555555556$$

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.

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