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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

5. Solving Quadratic Equations by Using the Quadratic Formula

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Exercise 26 Page 137

Make sure you write all the terms on the left-hand side of the equation before using the Quadratic Formula.

- 3.7, 1.1

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 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. - 3x^2 = 8x - 12 ⇕ - 3x^2 - 8x + 12 = 0 Now, we can identify the values of a, b, and c. - 3x^2 - 8x + 12=0 ⇕ - 3x^2+( - 8)x+ 12=0 We see that a= - 3, b= - 8, and c= 12. Let's substitute these values into the Quadratic Formula.

x=- b±sqrt(b^2-4ac)/2a

SubstituteValues

Substitute values

x=- ( -8)±sqrt(( - 8)^2-4( -3)( 12))/2( - 3)

▼

Solve for x and Simplify

- (- a)=a

x=8±sqrt((- 8)^2-4(- 3)(12))/2(- 3)

Calculate power

x=8±sqrt(64-4(- 3)(12))/2(- 3)

MultNegNegOnePar

- a(- b)=a* b

x=8±sqrt(64+12(12))/2(- 3)

a(- b)=- a * b

x=8±sqrt(64+12(12))/- 6

Multiply

x=8±sqrt(64+144)/- 6

Add terms

x=8±sqrt(208)/- 6

SplitIntoFactors

Split into factors

x=8±sqrt(16* 13)/- 6

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

x=8 ± sqrt(16)* sqrt(13)/-6

Calculate root

x=8 ± 4 sqrt(13)/-6

Factor out 2

x=2(4± 2sqrt(13))/-6

CancelCommonFac

Cancel out common factors

x=4 ± 2sqrt(13)/- 3

MoveNegDenomToFrac

Put minus sign in front of fraction

x=- 4 ± 2sqrt(13)/3

The solutions for this equation are x=- 4 ± 2sqrt(13)3. Let's separate them into the positive and negative cases.

x=- 4 ± 2sqrt(13)/3
x_1=- 4 + 2 sqrt(13)/3	x_2=- 4-2sqrt(13)/3
x_1≈ - 3.7	x_2≈ 1.1

Using the Quadratic Formula, we found that the solutions of the given equation are x_1 ≈ - 3.7 and x_2 ≈ 1.1.

Subchapter links

Exercises p.137-139