Answer:
x= -8,8
Step-by-step explanation:
Given: equation = [tex]x^2-64=0[/tex]
Solving [tex]x^2-64=0[/tex]
⇒(x+8)(x-8)=0
⇒x= -8,8
Square root property of equality state that if [tex]x^2=a,x=\sqrt{a}[/tex]
applying this property in equation [tex]x^2-64=0[/tex]
we get, [tex]x^2=64[/tex]
[tex]x=\sqrt{64}[/tex]
[tex]x=\pm8[/tex]
Isolate the variable:
we can isolate the variable in following steps
[tex]x^2-64=0[/tex] (given equation)
[tex]x^2=64[/tex] (add 64 both side)
then solve by square root property of equality as shown above
The solution to the equation x² - 64 = 0 by using the square root property of equality is ±8.
The square root property posits that if we have an expression with a perfect square solely on a single side and an integer on the other, we can calculate the problem by taking the square root from both sides and adding a plus or minus sign towards the side containing the number.
Thus, from the given equation, we have:
x² - 64 = 0
First, we isolate x²
x² = 64
[tex]\mathbf{(\sqrt{x})^2= \pm \sqrt{64} }[/tex]
x = ±8
Learn more about the square root property of equality here:
https://brainly.com/question/213768
