Exercise 21 Page 137

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 + 21x = - 18 ⇕ 5x^2 + 21x + 18 = 0 Now, we can identify the values of a, b, and c. 5x^2+ 21x+ 18=0 We see that a= 5, b= 21, and c= 18. Let's substitute these values into the Quadratic Formula.

x=- b±sqrt(b^2-4ac)/2a

SubstituteValues

Substitute values

x=- 21±sqrt(( 21)^2-4( 5)( 18))/2( 5)

▼

Solve for x and Simplify

CalcPow

Calculate power

x=- 21±sqrt(441-4(5)(18))/2(5)

Multiply

Multiply

x=- 21±sqrt(441-360)/10

SubTerm

Subtract term

x=- 21±sqrt(81)/10

CalcRoot

Calculate root

x=- 21 ± 9/10

The solutions for this equation are x= - 21± 910. Let's separate them into the positive and negative cases.

x=- 21± 9/10
x_1=- 21 + 9/10	x_2=-21 - 9/10
x_1=- 12/10	x_2=- 30/10
x_1=- 1.2	x_2=- 3

Using the Quadratic Formula, we found that the solutions of the given equation are x_1=-1.2 and x_2=- 3.