Question

Solve the equation with special factors.
x^2 - 81 = 0

Answer 1

Answer:

x = ± 9

Step-by-step explanation:

x² - 81 = 0 ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b) , then

x² - 81 = 0

x² - 9² = 0

(x - 9)(x + 9) = 0

Equate each factor to zero and solve for x

x - 9 = 0 ⇒ x = 9

x + 9 = 0 ⇒ x = - 9

Answer 2

Hello ShadowWolfie!

$\huge \boxed{\mathbb{QUESTION} \downarrow}$

Solve the equation with special factors.

x² - 81 = 0.

$\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}$

You can solve this question using 3 methods :-

1. By using the quadratic formula.
2. By finding the square root.
3. By using the difference of the squares.

Let's take a look at all the 3 methods.

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1. By Using Quadratic Formula :-

$x ^ { 2 } - 81 = 0$

We can use the biquadratic formula straight away as it is already in the form of ax² + bx + c. Now, we know that the biquadratic formula is :- $\frac{ - b \: ± \: \sqrt{ {b}^{2} - 4ac} }{2a}$. In this equation..

• a = x
• b = 0
• c = -81

Now, substitute these values in the formula..we get..

$\\ x=\frac{0±\sqrt{0^{2}-4\left(-81\right)}}{2}$

Let's simplify it.

$x=\frac{0±\sqrt{0^{2}-4\left(-81\right)}}{2} \\ x=\frac{0±\sqrt{-4\left(-81\right)}}{2} \\ x=\frac{0±\sqrt{324}}{2} \\ x=\frac{0±18}{2} \\ \boxed{\boxed{ \bf \: x = ±9}}$

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2. By Finding The Square Root :-

$x ^ { 2 } - 81 = 0$

Add zero to both the sides..our equation will become..

$x^{2}=81$

Now, take the square root on both the sides.

$x^{2}=81 \\ \sqrt{ {x}^{2} } = \sqrt{81} \\ \boxed{ \boxed{\bf x = ±9}}$

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3. By Using The Difference of The Squares :-

$x ^ { 2 } - 81 = 0$

Let's rewrite this equation as :- x² - 9². Now let's solve it using the algebraic identity ⇨ a² - b² = (a + b) (a - b). So..

$x ^ { 2 } - 81 = 0 \\ {x}^{2} - {9}^{2} = 0 \\ \left(x-9\right)\left(x+9\right)=0$

Let's solve for each term..

$(x - 9) = 0 \\ \underline{ \underline{x = + 9}}$

And..

$(x + 9) = 0 \\ \underline{ \underline{x = - 9}}$

So,

$\boxed{ \boxed{\bf x = ±9}}$

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• By using the 3 different methods (you can choose whichever method you find is easier), we got the answer as x = ± 9 .

__________________

Hope it'll help you!

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