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Algebra 2: 9x² = 25

by Ardesa
(New Smyrna Beach)











































9x² = 25

Solve the following equation for all solutions of x:

           9x² = 25

Check the answer by substitution the solution into the original equation

Comments for Algebra 2: 9x² = 25

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Nov 28, 2012
Solve for x
by: Staff


Answer

Part I


           9x² = 25

To solve for x, take the square root of each side of the equation

           √(9x²) = √(25)

           ±3x = ±5

           3x = ±5

Divide each side of the equation by 3

           3x / 3 = ±5 / 3

           x * (3 / 3) = ±5 / 3

           x * (1) = ±5 / 3

           x = ±5 / 3


Final Answer:

x = ±5 / 3

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Check the answer by substituting the two values of x into the original equation

If x = 5 / 3

           9x² = 25

           9(5/3)² = 25

           9(5²/3²) = 25

           9(25/9) = 25

           25 * (9/9) = 25

           25 * (1) = 25

           25 = 25, OK → x = 5 / 3 is a valid solution



If x = -5 / 3

           9x² = 25

           9(-5/3)² = 25

           9[(-5)²/3²] = 25

           9(25/9) = 25

           25 * (9/9) = 25

           25 * (1) = 25

           25 = 25, OK → x = -5 / 3 is a valid solution


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Nov 28, 2012
Solve for x
by: Staff

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Part II


You can also solve this equation using the difference of squares formula


The difference of squares formula states that:

(a + b)(a - b) = a² - b²

(a + b) and (a - b) are called conjugates.

This idea can be applied to your problem as follows:

           9x² = 25

           9x² - 25 = 25 - 25

           9x² - 25 = 0

           (3x)² - 5² = 0

Factor the left side of the equation

(3x + 5)(3x - 5) = 0

3x - 5 = 0

           3x - 5 + 5 = 0 + 5

           3x + 0 = 0 + 5

           3x = 5

           3x / 3 = 5 / 3

           x * (3 / 3) = 5 / 3

           x * (1) = 5 / 3

           x = 5 / 3


(3x + 5)(3x - 5) = 0

3x + 5 = 0

           3x + 5 - 5 = 0 - 5

           3x + 0 = 0 - 5

           3x = -5

           3x / 3 = -5 / 3

           x * (3 / 3) = -5 / 3

           x * (1) = -5 / 3

           x = -5 / 3

Again, the answer is

           x = ±5 / 3






Dec 11, 2012
Solve for x
by: Staff

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Part III

Math – graph of 9x² = 25







Thanks for writing.

Staff
www.solving-math-problems.com



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