x^2+250x-62500=0
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Answers
Answer:
Solve Quadratic Equation using the Quadratic Formula
x2+250x-62500 = 0 by the Quadratic Formula .
According to the Quadratic Formula, x , the solution for Ax2+Bx+C =0 where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 1
B = 250
C = -62500
Accordingly, B2 - 4AC =
62500 - (-250000) =
312500
Applying the quadratic formula :
-250 ± √ 312500
x = —————————
2
Can √ 312500 be simplified ?
Yes! The prime factorization of 312500 is
2•2•5•5•5•5•5•5•5
To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).
√ 312500 = √ 2•2•5•5•5•5•5•5•5 =2•5•5•5•√ 5 =
± 250 • √ 5
√ 5 , rounded to 4 decimal digits, is 2.2361
So now we are looking at:
x = ( -250 ± 250 • 2.236 ) / 2
Two real solutions:
x =(-250+√312500)/2=-125+125√ 5 = 154.508
or:
x =(-250-√312500)/2=-125-125√ 5 = -404.508
Answer:
Using Quadratic Formula:-
x2+250x-62500 = 0 by the Quadratic Formula .
According to the Quadratic Formula, x , the solution for Ax2+Bx+C =0 where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
x = ___________________
2A
In our case, A = 1
B = 250
C = -62500
Accordingly, B2 - 4AC =
62500 - (-250000) =
312500
Applying the quadratic formula :
-250 ± √ 312500
x = _____________________
2
=> √ 312500 be simplified ?
The prime factorization of 312500 is
2×2×5×5×5×5×5×5×5
√ 312500 = √ 2×2×5×5×5×5×5×5×5
=2×5×5×5×√ 5 =
± 250 × √ 5
√ 5 , rounded to 4 decimal digits, is 2.2361
So ,
x = ( -250 ± 250 • 2.236 ) / 2
real solutions:
x =(-250+√312500)/2=-125+125√ 5 = 154.508
or:
x =(-250-√312500)/2=-125-125√ 5 = -404.508