Answer:
x = 5, -5
Step-by-step explanation:
Find the roots of [tex]x^{2} -25=0[/tex] by solving for x.
Add 25 to both sides
[tex]x^{2} =25[/tex]
Square root both sides
[tex]x = 5[/tex]
[tex]x=-5[/tex]
The solution to the quadratic equation x² - 25 = 0 is 5, -5 after using the identity a² - b² = (a + b)(a - b).
Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
It is given that:
The quadratic equation:
x² - 25 = 0
As we know,
a² - b² = (a + b)(a - b)
Using the above identity:
x² - 5² = 0
(x + 5)(x - 5) = 0
x + 5 = 0
x = -5
Or
x - 5 = 0
x = 5
We can also find the solution to the equation x² - 25 = 0 using the quadratic formula.
Thus, the solution to the quadratic equation x² - 25 = 0 is 5, -5 after using the identity a² - b² = (a + b)(a - b).
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