Exercise 25 Page 349

To solve the given equation by factoring, we will start by writing all the terms on the left-hand side. Then, we will factor out the GCF. Afterwards, we will apply the Zero Product Property to solve the equation. Since the GCF is 1, we did not need to factor anything out in this situation. To find the solutions, we will solve the equation. Note that this is a quadratic equation. Thus, we will use the Quadratic Formula. ax^2+bx+c=0 ⇔ x=- b±sqrt(b^2-4ac)/2a To do so, we first need to identify a, b, and c. 4x^2+4x+1=0 ⇔ 4x^2+ 4x+ 1=0 We see that a= 4, b= 4, and c= 1. Let's substitute these values into the formula and solve for x.

x=- b±sqrt(b^2-4ac)/2a

SubstituteValues

Substitute values

x=- ( 4)±sqrt(( 4)^2-4( 4)( 1))/2( 4)

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Solve for x

CalcPow

Calculate power

x=- 4±sqrt(16-4(4)(1))/2(4)

Multiply

Multiply

x=- 4±sqrt(16-16)/8

SubTerms

Subtract terms

x=- 4±sqrt(0)/8

CalcRoot

Calculate root

x=- 4± 0/8

Note that adding and subtracting 0 will result in the same answer. Therefore, the equation will only have one solution. Solution x= - 4± 08= -48=- 12