Exercise 17 Page 161

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 We first need to identify the values of a, b, and c. 2x^2+x-15=0 ⇕ 2x^2+ 1x+( - 15)=0 We see that a= 2, b= 1, and c= - 15. Let's substitute these values into the Quadratic Formula.

x=- b±sqrt(b^2-4ac)/2a

SubstituteValues

Substitute values

x=- 1±sqrt(1^2-4( 2)( - 15))/2( 2)

▼

Solve for x and Simplify

CalcPow

Calculate power

x=- 1±sqrt(1-4(2)(- 15))/2(2)

Multiply

Multiply

x=- 1±sqrt(1-8(- 15))/4

MultNegNegOnePar

- a(- b)=a* b

x=- 1±sqrt(1+120)/4

AddTerms

Add terms

x=- 1±sqrt(121)/4

CalcRoot

Calculate root

x=- 1± 11/4

The solutions for this equation are x= - 1 ± 114. Let's separate them into the positive and negative cases.

x=- 1 ± 11/4
x_1=- 1 + 11/4	x_2=- 1 - 11/4
x_1=10/4	x_2=- 12/4
x_1=2.5	x_2=- 3

Using the Quadratic Formula, we found that the solutions of the given equation are x_1=- 3 and x_2=2.5.