Exercise 18 Page 195

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.

5x^2-9=11x

SubEqn

LHS-11x=RHS-11x

5x^2-11x-9=0

Now, we can identify the values of a, b, and c. 5x^2-11x-9=0 ⇔ 5x^2+( - 11)x+( - 9)=0 We see that a= 5, b= - 11, and c= - 9. Let's substitute these values into the Quadratic Formula.

x=- b±sqrt(b^2-4ac)/2a

SubstituteValues

Substitute values

x=- ( - 11)±sqrt(( - 11)^2-4( 5)( - 9))/2( 5)

▼

Solve for x and Simplify

NegNeg

- (- a)=a

x=11±sqrt((- 11)^2-4(5)(- 9))/2(5)

CalcPow

Calculate power

x=11±sqrt(121-4(5)(- 9))/2(5)

Multiply

Multiply

x=11±sqrt(121-20(- 9))/10

MultNegNegOnePar

- a(- b)=a* b

x=11±sqrt(121+180)/10

AddTerms

Add terms

x=11±sqrt(301)/10

Using the Quadratic Formula, we found that the solutions of the given equation are x= 11± sqrt(301)10. Therefore, the solutions are x_1= 11+sqrt(301)10 and x_2= 11-sqrt(301)10.