Exercise 47 Page 138

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.

2.3x^2 - 1.4x = 6.8

SubEqn

LHS-6.8=RHS-6.8

2.3x^2 - 1.4x - 6.8 = 0

MultEqn

LHS * 10=RHS* 10

23x^2 - 14x - 68 = 0

Now, we can identify the values of a, b, and c. 23x^2 - 14x - 68 = 0 ⇕ 23x^2+( - 14)x+( - 68)=0 We see that a= 23, b= - 14, and c= - 68. Let's substitute these values into the Quadratic Formula.

x=- b±sqrt(b^2-4ac)/2a

SubstituteValues

Substitute values

x=- ( -14)±sqrt(( - 14)^2-4( 23)( - 68))/2( 23)

▼

Solve for x and Simplify

NegNeg

- (- a)=a

x=14±sqrt((- 14)^2-4(23)(- 68))/2(23)

CalcPow

Calculate power

x=14±sqrt(196-4(23)(- 68))/2(23)

Multiply

Multiply

x=14±sqrt(196-92(- 68))/46

MultNegNegOnePar

- a(- b)=a* b

x=14±sqrt(196+6256)/46

AddTerms

Add terms

x=14±sqrt(6452)/46

SplitIntoFactors

Split into factors

x=14±sqrt(4* 1613)/46

SqrtProd

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

x=14± sqrt(4)* sqrt(1613)/46

CalcRoot

Calculate root

x=14± 2 sqrt(1613)/46

FactorOut

Factor out 2

x=2(7± sqrt(1613))/46

CancelCommonFac

Cancel out common factors

x=7± sqrt(1613)/23

The solutions for this equation are x= 7± sqrt(1613)23. Let's separate them into the positive and negative cases.

x=7± sqrt(1613)/23
x_1=7 + sqrt(1613)/23	x_2=7 - sqrt(1613)/23
x_1≈ 2.1	x_2 ≈ - 1.4

Using the Quadratic Formula, we found that the solutions of the given equation are x_1≈ 2.1 and x_2≈ - 1.4.