Algebra ->  Algebra  -> Quadratic Equations and Parabolas -> SOLUTION: Please help me solve this problem. 1. Type an exact answer, using radicals as needed. Rationalize all denominators. use a comma to seperate answeres as needed. 15x^4-8x^2+1      Log On

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1. Type an exact answer, using radicals as needed. Rationalize all denominators. use a comma to seperate answeres as needed.
15x^4-8x^2+1=0

Found 3 solutions by stanbon, Alan3354, psbhowmick:
You can put this solution on YOUR website!
Type an exact answer, using radicals as needed. Rationalize all denominators. use a comma to seperate answeres as needed.
15x^4-8x^2+1=0
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Think of two numbers whose product is 1*15 = 15
and whose sum is -8.
The numbers are -5 and -3
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Change the middle term of your problem to -5x-3x
15x^2-5x-3x+1 = 0
Factor the 1st 2 and the last two terms separately:
5x(3x-1)-(3x-1) = 0
Factor again:
(3x-1)(5x-1) = 0
Solve for "x":
x = 1/3 or x = 1/5
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cheers,
Stan H.

You can put this solution on YOUR website!
15x^4-8x^2+1=0
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x^2 = 1/5, 1/3
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x = +/- sqrt(5)/5
x = +/- sqrt(3)/3

You can put this solution on YOUR website!
The equation is .

Substitute .
Thus the equation becomes
Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: z=0.333333333333333,z=0.2. Graphical form: Equation was fully solved.Text form: 15*z^2-8*z+1=0 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( 15*z^2-8*z+1=0 )` If you have a website, here's a link to this solution.

### DETAILED EXPLANATION

Look at .
Equation is a quadratic equation: 15*z^2-8*z+1 =0, and has solutions 0.333333333333333,0.2
It becomes .
Result:
This is an equation! Solutions: z=0.333333333333333,z=0.2.

### Universal Simplifier and Solver

Done!

Thus z = , .
Hence, x = , i.e. ,