x^2-4x-21=0
how do you solve this
x ^ 2 - 4 x - 21 = 0 Add 21 to both sides
x ^ 2 - 4 x - 21 + 21 = 0 + 21
x ^ 2 - 4 x = 21 Add 4 to both sides
x ^ 2 - 4 x + 4 = 21 + 4
x ^ 2 - 4 x + 4 = 25
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Remark :
( a - b ) ^ 2 = a ^ 2 - 2 a b + b ^ 2
That's why :
x ^ 2 - 4 x + 4 = ( x - 2 ) ^ 2
x ^ 2 - 4 x + 4 = 25
( x - 2 ) ^ 2 = 25
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( x - 2 ) ^ 2 = 25
x - 2 = + OR - sqrt ( 25 )
Fist solution :
x - 2 = sqrt ( 25 )
x - 2 = 5 Add 2 to both sides
x - 2 + 2 = 5 + 2
x = 7
Second solution :
x - 2 = - sqrt ( 25 )
x - 2 = - 5 Add 2 to both sides
x - 2 + 2 = - 5 + 2
x = - 3
Solutions are :
x = - 3
and
x = 7
yea that's pretty much it!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!111111
To solve the quadratic equation x^2 - 4x - 21 = 0, you can use the quadratic formula, which states that for an equation in the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / 2a
For the given equation, a = 1, b = -4, and c = -21. Plugging these values into the quadratic formula, we have:
x = (4 ± √((-4)^2 - 4(1)(-21))) / (2(1))
Simplifying further:
x = (4 ± √(16 + 84)) / 2
x = (4 ± √100) / 2
x = (4 ± 10) / 2
This gives us two possible values for x:
x = (4 + 10) / 2 = 14 / 2 = 7
x = (4 - 10) / 2 = -6 / 2 = -3
Therefore, the solutions to the equation x^2 - 4x - 21 = 0 are x = 7 and x = -3.