Solve the quadratic equation. 9) 9x2 - 4 = 0?

Very basic. Do not forget the ±

9x² = 4

x² = 4/9

x = ±√(4/9) = ± 2/3

You can also do by factoring, but only because both numbers are squares. If even one of them were not, you would need to use this technique.

Difference of two squares: a^2 - b^2 = (a + b)(a - b)

9x^2 - 4 = 0 (factor as difference of two squares)
(3x + 2)(3x - 2) = 0 (zero-product property)
3x + 2 = 0 or 3x - 2 = 0
3x = -2 or 3x = 2
x = -2/3 or x = 2/3 <===ANSWER

or you could solve it this way

9x^2 - 4 = 0 (add 4 to both sides)
9x^2 = 4 (divide both sides by 9)
x^2 = 4/9 (square root both sides)
x = +/- 2/3 <===ANSWER

2/3 or -2/3

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RE:
Solve the quadratic equation. 9) 9x2 - 4 = 0?

9x^2 = 4

x^2 = 4/9

x = ± (2/3)

a^2 - b^2 ≡ (a + b)(a - b)

9x^2 - 4 = 0
(3x)^2 - 2^2 = 0
(3x + 2)(3x - 2) = 0

3x + 2 = 0
3x = -2
x = -2/3

3x - 2 = 0
3x = 2
x = 2/3

∴ x = ±2/3

Add 4 to both sides:
9x^2=4

Divide both sides by 9:
x^2=4/9

Take the square root of both sides:
x= +/- 2/3 so x=2/3 or x= -2/3 (answer)

You could do this by using the quadratic formula if you wanted. Refer to my Math Variety blog post on how to solve quadratic equations by using the quadratic formula. I have an explanation of what the quadratic formula is, practice problems, and solutions.
http://mathvariety.blogspot.com/2009/04/solving-quadratic-equations-by-using.html
http://mathvariety.blogspot.com/2009/05/solving-quadratic-equations-by-using.html
http://mathvariety.blogspot.com/2009/05/solving-quadratic-equations-by-using_24.html


Check out my eHow article on how to solve quadratic equations by using the quadratic formula:
http://www.ehow.com/how_4816180_quadratic-equation-using-quadratic-formula.html

Also check out this link. It’s a calculator that will give you the roots (solutions) to any quadratic equation. Just enter values for a, b, and c.
http://www.1728.com/quadratc.htm

The quadratic formula is:
x = [-b +/- sqrt(b^2-4ac)]/(2a)

This is the difference of squares.
9x² - 4 = (3x)² - (2)²
= (3x+2)(3x-2)
x = ±2/3

x^2 = 4/9

x = +/- 2/3

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