Exercise 27 Page 349

To solve the given equation by factoring, we will start by writing all the terms on the left-hand side as a polynomial in standard form. Then, we will apply the Quadratic Formula to solve the equation.

Factoring using the Quadratic Formula

We will use the Quadratic Formula to find the factors. To do so, we will need to identify the values of a, b, and c. 2x^2 -4x+ 3=0 We can see above that a= 2, b= -4, and c= 3. Finally, we will substitute these values into the Quadratic Formula.

x=- b±sqrt(b^2-4ac)/2a

SubstituteValues

Substitute values

x=- ( -4)±sqrt(( -4)^2-4( 2)( 3))/2( 2)

▼

Solve for x and Simplify

NegNeg

- (- a)=a

x=4±sqrt((-4)^2-4(2)(3))/2(2)

CalcPow

Calculate power

x=4±sqrt(16-4(2)(3))/2(2)

Multiply

Multiply

x=4±sqrt(16-24)/4

SubTerm

Subtract term

x=4±sqrt(-8)/4

SplitIntoFactors

Split into factors

x=4±sqrt(- 1* 2* 4)/4

SqrtProd

sqrt(a* b)=sqrt(a)*sqrt(b)

x=4 ± sqrt(- 1) sqrt(2) sqrt(4)/4

SqrtNegOneToI

sqrt(- 1)= i

x=4 ± isqrt(2) sqrt(4)/4

CalcRoot

Calculate root

x=4 ± 2isqrt(2)/4

SimpTerms

Simplify terms

x=2 ± isqrt(2)/2