SOLUTION: p^2+3/4p+1/4=0

Question 296154: p^2+3/4p+1/4=0
Answer by persian52(161) (Show Source): You can put this solution on YOUR website!
p^(2)+(3)/(4)*p+(1)/(4)=0
Multiply (3)/(4) by p to get (3p)/(4).
p^(2)+(3p)/(4)+(1)/(4)=0
Combine all similar expressions.
p^(2)+(3p+1)/(4)=0
Multiply each term by a factor of 1 that will equate all the denominators. In this case, all terms need a denominator of 4.
p^(2)*(4)/(4)+(3p+1)/(4)=0
Multiply p^(2) by 4 to get 4p^(2).
(4p^(2))/(4)+(3p+1)/(4)=0
The numerators of expressions that have equal denominators can be combined. In this case, ((4p^(2)))/(4) and ((3p+1))/(4) have the same denominator of 4, so the numerators can be combined.
((4p^(2))+(3p+1))/(4)=0
Combine all similar expressions in the polynomial.
(4p^(2)+3p+1)/(4)=0
Multiply each term in the equation by 4.
4p^(2)+3p+1=0
Use the quadratic formula to find the solutions. In this case, the values are a=4, b=3, and c=1.
p=(-b\~(b^(2)-4ac))/(2a) where ap^(2)+bp+c=0
Substitute in the values of a=4, b=3, and c=1.
p=(-3\~((3)^(2)-4(4)(1)))/(2(4))
Simplify the section inside the radical.
p=(-3\i~(7))/(2(4))
Simplify the denominator of the quadratic formula.
p=(-3\i~(7))/(8)
Simplify the expression to solve for the + portion of the \.
p=(-3+i~(7))/(8)
Simplify the expression to solve for the - portion of the \.
p=(-3-i~(7))/(8)
The final answer is the combination of both solutions.
p=(-3+i~(7))/(8),(-3-i~(7))/(8)
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