Exercise 49 Page 230

To solve the given equation, let's factor and solve using the Zero Product Property.

Factoring

Let's get factoring!

x^2+4x=0

FactorOut

Factor out x

x(x+4)=0

Solving

Now we can apply the Zero Product Property to solve.

x(x+4)=0

ZeroProdProp

Use the Zero Product Property

lcx=0 & (I) x+4=0 & (II)

SubEqn

(II): LHS-4=RHS-4

lx_1=0 x_2=- 4

The solutions for our equation are 0 and - 4.

Checking Our Answer

Checking our answer

To check our answers, we will substitute them for x in the given equation. Let's start with x=0.

x^2+4x=0

Substitute

x= 0

( 0)^2+4( 0)? =0

CalcPow

Calculate power

0+4(0)? =0

ZeroPropMult

Zero Property of Multiplication

0=0 ✓

Since substituting and solving resulted in a true statement, we know that x=0 is a solution of the equation. Let's now check x=- 4.

x^2+4x=0

Substitute

x= - 4

( - 4)^2+4( - 4)? =0

CalcPow

Calculate power

16+4(- 4)? =0

MultPosNeg

a(- b)=- a * b

16-16? =0

SubTerm

Subtract term

0=0 ✓

This is also a true statement, so we know that x=- 4 is a solution of the equation.

Hints

Check the answer

Practice exercises

Asses your skill

Factoring

Solving

Checking Our Answer