Exercise 2 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 To do so, we first need to identify the values of a, b, and c. x^2-10x+16=0 ⇔ 1x^2+( - 10)x+ 16=0 We see that a= 1, b= - 10, and c= 16. Let's substitute these values into the Quadratic Formula. Be careful with the signs!

x=- b±sqrt(b^2-4ac)/2a

SubstituteValues

Substitute values

x=- ( -10)±sqrt(( - 10)^2-4( 1)( 16))/2( 1)

▼

Solve for x and Simplify

NegNeg

- (- a)=a

x=10±sqrt((- 10)^2-4(1)(16))/2(1)

CalcPow

Calculate power

x=10±sqrt(100-4(1)(16))/2(1)

MultByOne

a * 1=a

x=10±sqrt(100-4(16))/2

MultNegPos

(- a)b = - ab

x=10±sqrt(100-64)/2

SubTerm

Subtract term

x=10±sqrt(36)/2

CalcRoot

Calculate root

x=10± 6/2

The solutions for this equation are x= 10± 62. Let's separate them into the positive and negative cases.

x=10± 6/2
x_1=10+ 6/2	x_2=10- 6/2
x_1=16/2	x_2=4/2
x_1=8	x_2=2

Using the Quadratic Formula, we found that the solutions of the given equation are x_1=8 and x_2=2.