Question

(x2 + 4x + 3) = (x + 3)​

Answer 1

Method 1: Solve by Factoring

Let's solve your equation step-by-step.

$(x^2+4x+3)=(x+3)$

Step 1: Subtract $x+3$ from both sides.

$(x^2+4x+3)-(x+3)=(x+3)-(x+3)$

$x^2+3x=0$

Step 2: Factor left side of the equation.

$x(x+3)=0$

Step 3: Set factors equal to 0.

$x=0\ or \ x+3=0$

$x=0\ or \ x=-3$

Method 2: Solve with the Quadratic Formula

Let's solve your equation step-by-step.

$(x^2+4x+3)=(x+3)$

Step 1: Subtract $x+3$ from both sides.

$(x^2+4x+3)-(x+3)=(x+3)-(x+3)$

$x^2+3x=0$

For this equation:

$a=1\\ b=3\\ c=0$

$1x^2+3x+0=0$

Step 2: Use quadratic formula with a=1, b=3, c=0.

$x=\frac{-b\±\sqrt{b^2-4ac} }{2a}$

$x=\frac{-(3)\± \sqrt{3^2-4(1)(0)} }{2(1)}$

$x=\frac{-3\± \sqrt{9} }{2}$

$x=0\ or \ x=-3$

Method 3: Solve by Completing Square

Let's solve your equation step-by-step.

$x^2+4x+3=x+3$

Step 1: Subtract x from both sides.

$x^2+4x+3-x=x+3-x$

$x^2+3x+3=3$

Step 2: Subtract 3 from both sides.

$x^2+3x+3-3=3-3$

$x^2+3x=0$

Step 3: The coefficient of 3x is 3. Let b=3.

Then we need to add $(\frac{b}{2} )^2=\frac{9}{4}$ to both sides to complete the square.

Add $\frac{9}{4}$ to both sides.

$x^2+3x+\frac{9}{4} =0+\frac{9}{4}$

$x^2+3x+\frac{9}{4}=\frac{9}{4}$

Step 4: Factor left side.

$(x+\frac{3}{2})^2=\frac{9}{4}$

Step 5: Take the square root.

$x+\frac{3}{2}=\± \sqrt{\frac{9}{4} }$

Step 6: Add $\frac{-3}{2}$ to both sides.

$x+\frac{3}{2}+\frac{-3}{2} =\frac{-3}{2} \± \sqrt{\frac{9}{4} }$

$x=\frac{-3}{2} \±\sqrt{\frac{9}{4} }$

$x=0\ or \ x=-3$

∴ $x=0\ or \ x=-3$ in the equation ⇒ $(x^2+4x+3)=(x+3)$