Question 28876: -2x squared + 10x = 15
Answer by sdmmadam@yahoo.com(530)   (Show Source):
You can put this solution on YOUR website! -2x squared + 10x = 15
Multiplying by (-1),we have,
2x^2-10x=-15
2x^2-10x+15 = 0 ----(1)
x = {-(-10) + or minus sqrt[(-10)^2 - 4X(2)X(15)]}/[2X(2)]
[Using x =[(-b)+or minus sqrt(b^2-4ac)]/2a for the given equation:(ax^2+bx+c)=0]
x={10+or minus sqrt(100-120)}/4
x=(1/4)X[10+ or minus sqrt(-20)]
x=(1/4)X[10+ or minus (2isqrt(5))]
x=(1/2)X[5+ or minus isqrt(5)] (cancelling 2 in the nr and dr )
Therefore the values are
x=[5+ i sqrt(5)]/2 and x=[5 - i sqrt(5)]/2
[sqrt(-20)= sqrt(5X4Xi^2)=sqrt(5X2^2i^2)=2i(sqrt(5))]
Verification: x=[5+ i sqrt(5)]/2 in (1)
LHS = 2x^2-10x+15
=2X {[5+ i sqrt(5)]/2 }^2-10X{[5+ i sqrt(5)]/2} +15
=2X{25+5i^2+10isqrt(5)}/4 -25-5isqrt(5) +15
=(25/2)+5/2X(-1)+5isqrt(5)-25-5isqrt(5)+15
=25/2-5/2-25+15
=(20/2)-10
=10-10
=0
=RHS
Therefore the above value of x is correct.
Complex roots always occur in conjugate pairs.
Hence no need to check for the validity of the other value of x.
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