Exercise 17 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.

4x^2-9=- 7x-4

AddEqn

LHS+7x=RHS+7x

4x^2+7x-9=- 4

AddEqn

LHS+4=RHS+4

4x^2+7x-5=0

Now, we can identify the values of a, b, and c. 4x^2+7x-5=0 ⇔ 4x^2+ 7x+( - 5)=0 We see that a= 4, b= 7, and c= - 5. Let's substitute these values into the Quadratic Formula.

x=- b±sqrt(b^2-4ac)/2a

SubstituteValues

Substitute values

x=- 7±sqrt(7^2-4( 4)( - 5))/2( 4)

▼

Solve for x and Simplify

CalcPow

Calculate power

x=- 7±sqrt(49-4(4)(- 5))/2(4)

Multiply

Multiply

x=- 7±sqrt(49-16(- 5))/8

MultNegNegOnePar

- a(- b)=a* b

x=- 7±sqrt(49+80)/8

AddTerms

Add terms

x=- 7±sqrt(129)/8

Using the Quadratic Formula, we found that the solutions of the given equation are x= - 7± sqrt(129)8. Therefore, the solutions are x_1= - 7+sqrt(129)8 and x_2= - 7-sqrt(129)8.