Exercise 14 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.

x^2+45x=- 200

AddEqn

LHS+200=RHS+200

x^2+45x+200=0

Now, we can identify the values of a, b, and c. x^2+45x+200=0 ⇔ 1x^2+ 45x+ 200=0 We see that a= 1, b= 45, and c= 200. Let's substitute these values into the Quadratic Formula.

x=- b±sqrt(b^2-4ac)/2a

SubstituteValues

Substitute values

x=- 45±sqrt(45^2-4( 1)( 200))/2( 1)

▼

Solve for x and Simplify

CalcPow

Calculate power

x=- 45±sqrt(2025-4(1)(200))/2(1)

Multiply

Multiply

x=- 45±sqrt(2025-800)/2

SubTerm

Subtract term

x=- 45±sqrt(1225)/2

CalcRoot

Calculate root

x=- 45± 35/2

The solutions for this equation are x= - 45± 352. Let's separate them into the positive and negative cases.

x=- 45± 35/2
x_1=- 45+35/2	x_2=- 45-35/2
x_1=- 10/2	x_2=- 80/2
x_1=- 5	x_2=- 40

Using the Quadratic Formula, we found that the solutions of the given equation are x_1=- 5 and x_2=- 40.