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McGraw Hill Integrated II, 2012

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McGraw Hill Integrated II, 2012 View details

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Exercise 10 Page 713

Recall the Quadratic Formula and use it to solve the given equation.

- 2.4, 1.6

Practice makes perfect

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 aWe first need to identify the values of a, b, and c. 5x^2+4x-20=0 ⇕ 5x^2+ 4x+( - 20)=0 We see that a= 5, b= 4, and c= - 20. Let's substitute these values into the Quadratic Formula.

x=- b±sqrt(b^2-4ac)/2a

SubstituteValues

Substitute values

x=- 4±sqrt(4^2-4( 5)( - 20))/2( 5)

▼

Solve for x and Simplify

Calculate power

x=- 4±sqrt(16-4(5)(- 20))/2(5)

a(- b)=- a * b

x=- 4±sqrt(16-20(- 20))/10

MultNegNegOnePar

- a(- b)=a* b

x=- 4±sqrt(16+400)/10

Add terms

x=- 4±sqrt(416)/10

SplitIntoFactors

Split into factors

x=- 4±sqrt(16* 26)/10

sqrt(a* b)=sqrt(a)*sqrt(b)

x=- 4± sqrt(16)* sqrt(26)/10

Calculate root

x=- 4± 4sqrt(26)/10

Factor out 2

x=2(- 2± 2sqrt(26))/10

CancelCommonFac

Cancel out common factors

x=- 2± 2sqrt(26)/5

Using the Quadratic Formula, we found that the solutions of the given equation are x= - 2± 2sqrt(26)5. Therefore, the solutions are x_1= - 2+2sqrt(26)5≈ 1.6 and x_2= - 2-2sqrt(26)5≈ - 2.4.

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