SOLUTION: Hello im stuck in this problem The questions is simple Solve the equation [6^(1/2)]x^2+2x-[(3/2)^(1/2)]=0 The six is squareooted by itself with the x^2 outside the squareroot,

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Hello im stuck in this problem The questions is simple Solve the equation [6^(1/2)]x^2+2x-[(3/2)^(1/2)]=0 The six is squareooted by itself with the x^2 outside the squareroot,       Log On


   



Question 878849: Hello im stuck in this problem
The questions is simple
Solve the equation
[6^(1/2)]x^2+2x-[(3/2)^(1/2)]=0
The six is squareooted by itself with the x^2 outside the squareroot, and the 3/2 are inside the squareroot

Answer by AnlytcPhil(1810) About Me  (Show Source):
You can put this solution on YOUR website!
%28sqrt%286%29%29x%5E2%2B2x-sqrt%283%2F2%29%22%22=%22%22%220%22

Simplify sqrt%283%2F2%29%29%22%22=%22%22sqrt%28%283%2A2%29%2F%282%2A2%29%29%22%22=%22%22sqrt%286%29%2Fsqrt%284%29%22%22=%22%22sqrt%286%29%2F2

%28sqrt%286%29%29x%5E2%2B2x-sqrt%286%29%2F2%22%22=%22%22%220%22

Clear the fraction by multiplying through by 2

%282sqrt%286%29%29x%5E2%2B4x-sqrt%286%29%22%22=%22%22%220%22

Use the quadratic formula:

x%22%22=%22%22%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

with

a=2sqrt%286%29, b=4, c=-sqrt%286%29

x%22%22=%22%22

x%22%22=%22%22%28-4+%2B-+sqrt%2816%2B48%29%29%2F%284%2Asqrt%286%29%29+

x%22%22=%22%22%28-4+%2B-+sqrt%2864%29%29%2F%284%2Asqrt%286%29%29+

x%22%22=%22%22%28-4+%2B-+8%29%2F%284%2Asqrt%286%29%29+

x%22%22=%22%22%28-4+%2B-+8%29%2F%284%2Asqrt%286%29%29+

Using the +

x%22%22=%22%22%28-4+%2B+8%29%2F%284sqrt%286%29%29+

x%22%22=%22%224%2F%284%2Asqrt%286%29%29+

x%22%22=%22%221%2F%28sqrt%286%29%29%29+

x%22%22=%22%22%281%2F%28sqrt%286%29%29%29%28sqrt%286%29%2Fsqrt%286%29%29+

x%22%22=%22%22sqrt%286%29%2F6

Using the -

x%22%22=%22%22%28-4+-+8%29%2F%284sqrt%286%29%29+

x%22%22=%22%22-12%2F%284%2Asqrt%286%29%29+

x%22%22=%22%22-3%2F%28sqrt%286%29%29%29+

x%22%22=%22%22%28-3%2F%28sqrt%286%29%29%29%28sqrt%286%29%2Fsqrt%286%29%29+

x%22%22=%22%22-3sqrt%286%29%2F6

x%22%22=%22%22-sqrt%286%29%2F2

Two solutions:  sqrt%286%29%2F6, -sqrt%286%29%2F2

Edwin