Exercise 39 Page 160

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. 21x^2+5x-7=0 ⇕ 21x^2+ 5x+( - 7)=0 We see that a= 21, b= 5, and c= - 7. Let's substitute these values into the Quadratic Formula.

x=- b±sqrt(b^2-4ac)/2a

SubstituteValues

Substitute values

x=- ( 5)±sqrt(5^2-4( 21)( - 7))/2( 21)

▼

Solve for x and Simplify

MultPropNegOne

Multiplication Property of -1

x=-5±sqrt(5^2-4(21)(-7))/2(21)

CalcPow

Calculate power

x=-5±sqrt(25-4(21)(-7))/2(21)

Multiply

Multiply

x=-5±sqrt(25-84(-7))/42

MultNegNegOnePar

- a(- b)=a* b

x=-5±sqrt(25+588)/42

AddTerms

Add terms

x=-5±sqrt(613)/42

The solutions for this equation are x= -5±sqrt(613)42. Let's separate them into positive and negative cases.

x=-5±sqrt(613)/42
x_1=-5+sqrt(613)/42	x_2=-5-sqrt(613)/42
x_1≈-5+24.75/42	x_2≈-5-24.75/42
x_1≈19.75/42	x_2≈-29.75/42
x_1≈0.5	x_2≈-0.7

Using the Quadratic Formula, we found that the solutions of the given equation are x_1≈0.5 and x_2≈-0.7.