Exercise 22 Page 356

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.

x^2-7x=8

SubEqn

LHS-8=RHS-8

x^2-7x-8=0

Now, we can identify the values of a, b, and c. x^2-7x-8=0 ⇔ 1x^2+( -7)x+( - 8)=0 We see that a= 1, b= - 7, and c= - 8. 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( 1)( - 8))/2( 1)

▼

Solve for x and Simplify

NegNeg

- (- a)=a

x=7±sqrt((- 7)^2-4(1)(- 8))/2(1)

CalcPow

Calculate power

x=7±sqrt(49-4(1)(- 8))/2(1)

MultByOne

a * 1=a

x=7±sqrt(49-4(-8))/2

MultNegNegOnePar

- a(- b)=a* b

x=7±sqrt(49+32)/2

AddTerms

Add terms

x=7±sqrt(81)/2

CalcRoot

Calculate root

x=7± 9/2

The solutions for this equation are x= 7± 92. Let's separate them into positive and negative cases.

x=7± 9/2
x_1=7+9/2	x_2=7-9/2
x_1=16/2	x_2=-2/2
x_1=8	x_2=-1

Using the Quadratic Formula, we found that the solutions of the given equation are x_1=8 and x_2=-1.