Exercise 24 Page 137

We will use the Quadratic Formula to solve the given quadratic equation. ax^2+ bx+ c=0 ⇔ x=- b± sqrt(b^2-4 a c)/2 a Let's start by rewriting the equation so all of the terms are on the left-hand side and then simplify as much as possible.

4x^2=-16x-16

AddEqn

LHS+16x=RHS+16x

4x^2+16x=-16

AddEqn

LHS+16=RHS+16

4x^2+16x+16=0

FactorOut

Factor out 4

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

DivEqn

.LHS /4.=.RHS /4.

x^2+4x+4=0

Now, we can identify the values of a, b, and c. x^2+4x+4=0 ⇔ 1x^2+ 4x+ 4=0 We see that a= 1, b= 4, and c= 4. Let's substitute these values into the Quadratic Formula.

x=- b±sqrt(b^2-4ac)/2a

SubstituteValues

Substitute values

x=- 4±sqrt(4^2-4( 1)( 4))/2( 1)

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Solve for x and Simplify

CalcPow

Calculate power

x=-4±sqrt(16-4(1)(4))/2(1)

MultByOne

a * 1=a

x=-4±sqrt(16-4(4))/2

MultNegPos

(- a)b = - ab

x=-4±sqrt(16-16)/2

SubTerm

Subtract term

x=-4±sqrt(0)/2

CalcRoot

Calculate root

x=-4± 0/2

AddSubTerms

Add and subtract terms

x=-4/2

MoveNegNumToFrac

Put minus sign in front of fraction

x=- 4/2

CalcQuot

Calculate quotient

x=-2

Using the Quadratic Formula, we found that the only solution of the equation is x=-2.