SOLUTION: s^2+6s+25= solve for Solution sets 2x^2-9x=1 solve for x Can you show me how you find the answer, not just the answer?

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Question 37567: s^2+6s+25= solve for Solution sets
2x^2-9x=1
solve for x
Can you show me how you find the answer, not just the answer?

Answer by junior403(76) About Me  (Show Source):
You can put this solution on YOUR website!
s^2+6s+25= solve for Solution sets
The s^2 indicates there will be 2 solutions.
Besure that the quadratic equation is equal to zero.
Use quadratic formula to solve.
In this case...
s^2+6s+25=0
s=%28-b%2B-sqrt%28b%5E2-4%2Aa%2Ac%29%29%2F%282%2Aa%29
ax^2+bx+c=0
plug in your variables
a=1 b=6 c=25
So...
s=%28-6%2B-sqrt%286%5E2-4%2A1%2A25%29%29%2F%282%2A1%29
and...
s=%28-6%2B-sqrt%2836-100%29%29%2F%282%29
and...
s=%28-6%2B-sqrt%28-64%29%29%2F%282%29
The negative number beneith the radical will result in an imaginary expression.
Thus...
s=%28-6%2B-+i%2A+sqrt%2864%29%29%2F%282%29
So...
s=%28-6%2B-+i%2A+8%29%2F%282%29
or...
s=%28-6%2B-+8i%29%2F%282%29
Remember, first factor out the 2 in the numerator and then cancel...
s=%282%2A-3%2B-+4i%29%2F%282%29
and...
s=%28-3%2B-+4i%29
So the solution set is...
{-3+4i,-3-4i}
So for the equation...
2x^2-9x=1
Use the same process first making equation equal to zero.
So...
2x^2-9x=1 (subtract 1 from both sides of the equation then begin)
2x^2-9x-1=0
Again x^2 indicates 2 solutions
Use quadratic formula by plugging in indicated variables
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=2 b=-9 c=-1 (remember -b means the OPPOSITE of the value of b)
So...
x+=+%289+%2B-+sqrt%28+-9%5E2-4%2A2%2A-1+%29%29%2F%282%2A2%29+
Then...
x+=+%289+%2B-+sqrt%28+81%2B8+%29%29%2F%284%29+
And...
x+=+%289+%2B-+sqrt%28+89+%29%29%2F%284%29+
89 is aprime number so there is no square root.
So you final result is the solution set...
%289+%2B+sqrt%28+89+%29%29%2F%284%29, %289+-+sqrt%28+89+%29%29%2F%284%29