Guys how can i solve this quadratic equation?

Question

i am used to solving quadratic equation with the quadratic formula, but i had a little problem with these quadratic equation.

here:
x^2 -25=0

here is another one
x^2 + 8x=0

my problem is.... do i have to use the formula to work this out??
Explain....In simplest way...Thanks!

x^2 is x square

Answer 1

Question 1
x ² = 25
x = ± 5

Question 2
x = [ - 8 ± √64 ] / 2
x = [ - 8 ± 8 ] / 2
x = 0 , x = - 8
OR
x (x + 8) = 0
x = 0 , x = - 8

Answer 2

These can both still be solved with the quadratic formula

x² - 25 = 0 is equivalent to x² + 0x - 25 = 0 (b = 0)
x² + 8x = 0 is equivalent to x² + 8x + 0 = 0 (c = 0)

Of course, a simpler way would be to factorise them

x² - 25 = 0
(x + 5)(x - 5) = 0
x + 5 = 0 or x - 5 = 0
x = ±5

x² + 8x = 0
x(x + 8) = 0
x = 0 or x + 8 = 0
x = {0, -8}

Answer 3

The quadratic formula will work, of course, but both of these can be handled much more easily. Firstly, x^2-25 factors into (x-5)(x+5), so the roots are + and -5. Secondly, x^2 + 8x factors into x(x+8), so the roots are 0 and -8.

Answer 4

The first example is a difference of two squares. You need to be able to spot these. If you are presented with something like

a^2 - b^2

it will always factorise into (a+b)(a-b).

a^2 - b^2 = (a+b)(a-b) - learn it.

The second, you can start by taking the x out equation, so

x^2 + 8x = 0
=> x(x+8) = 0... (*)

Remember, you cannot divide by x - since x could be zero.

From (*) you can then say, since the two factors (x and x+8) mutliply to give zero, one of them must be zero for the equation to be satisfied.

so x=0, or
x+8=0 => x=-8.

Hope that was simple enough!

Answer 5

x^2 -- 25 = 0
=> x^2 = 25
=> x^2 = 5^2
=> x = sqrt(5^2) = 5, --5

x^2 + 8x = 0
=> x(x + 8) = 0 giving
x = 0 or
x + 8 = 0 => x = --8

Answer 6

x^2 - 25 = 0

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

x is = to either -5 or 5

x^2 + 8x - 0

x(x + 8) = 0

x = 0 or x = -8

This is just factorising quadratic equations (using the simplest method).

Answer 7

oh ok
1. x^2=25
x= square root of 25
x=5
2. x^2 +8x=0
factorise
x(x + 8) = 0
so X=o
and x+8=0
take 8 over
X = -8

so answer is x=0, x=-8

Answer 8

first one is difference of two squares

(x-5)(x+5) = 0 so x = 5 or -5

second one x is a factor in both so take it outside

x(x+8) = 0

leaving a simple linear equation, so x = 0 or x= -8


The quadratic formula will still work on these equations just remember b =0 in the first one and c=0 in the second

Answer 9

x^2 -25=0
(x+5)(x-5) = 0, by factorizing

so x=5, -5

x^2 + 8x=0
x(x+8)=0, by factorizing
so, x=0 or -8

Answer 10

x^2 - 25 = 0
(x + 5) (x - 5)

Answer: x = 5, x = - 5

x^2 + 8x = 0
x (x + 8) = 0

Answer: x = - 8, x = 0