16x^4-20x^2+5=0

Simple and best practice solution for 16x^4-20x^2+5=0 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 16x^4-20x^2+5=0 equation:


Simplifying
16x4 + -20x2 + 5 = 0

Reorder the terms:
5 + -20x2 + 16x4 = 0

Solving
5 + -20x2 + 16x4 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
16 the coefficient of the squared term: 

Divide each side by '16'.
0.3125 + -1.25x2 + x4 = 0

Move the constant term to the right:

Add '-0.3125' to each side of the equation.
0.3125 + -1.25x2 + -0.3125 + x4 = 0 + -0.3125

Reorder the terms:
0.3125 + -0.3125 + -1.25x2 + x4 = 0 + -0.3125

Combine like terms: 0.3125 + -0.3125 = 0.0000
0.0000 + -1.25x2 + x4 = 0 + -0.3125
-1.25x2 + x4 = 0 + -0.3125

Combine like terms: 0 + -0.3125 = -0.3125
-1.25x2 + x4 = -0.3125

The x term is -1.25x2.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25x2 + 0.390625 + x4 = -0.3125 + 0.390625

Reorder the terms:
0.390625 + -1.25x2 + x4 = -0.3125 + 0.390625

Combine like terms: -0.3125 + 0.390625 = 0.078125
0.390625 + -1.25x2 + x4 = 0.078125

Factor a perfect square on the left side:
(x2 + -0.625)(x2 + -0.625) = 0.078125

Calculate the square root of the right side: 0.279508497

Break this problem into two subproblems by setting 
(x2 + -0.625) equal to 0.279508497 and -0.279508497.

Subproblem 1

x2 + -0.625 = 0.279508497 Simplifying x2 + -0.625 = 0.279508497 Reorder the terms: -0.625 + x2 = 0.279508497 Solving -0.625 + x2 = 0.279508497 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x2 = 0.279508497 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x2 = 0.279508497 + 0.625 x2 = 0.279508497 + 0.625 Combine like terms: 0.279508497 + 0.625 = 0.904508497 x2 = 0.904508497 Simplifying x2 = 0.904508497 Take the square root of each side: x = {-0.951056516, 0.951056516}

Subproblem 2

x2 + -0.625 = -0.279508497 Simplifying x2 + -0.625 = -0.279508497 Reorder the terms: -0.625 + x2 = -0.279508497 Solving -0.625 + x2 = -0.279508497 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x2 = -0.279508497 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x2 = -0.279508497 + 0.625 x2 = -0.279508497 + 0.625 Combine like terms: -0.279508497 + 0.625 = 0.345491503 x2 = 0.345491503 Simplifying x2 = 0.345491503 Take the square root of each side: x = {-0.587785252, 0.587785252}

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.951056516, 0.951056516, -0.587785252, 0.587785252}

See similar equations:

| 6x^2-600=0 | | 5x=7x-10 | | 2x^2-15x-8=0 | | 6x+7=5x+15 | | -8-9=-8(x-9) | | 64x-1=0 | | 2x+107=10x-5 | | 2x^6+4x^5-6x^4+4x^3= | | 4x-y=-1 | | 73-3x=15x+17 | | 3x-4(1-x)=4+5x | | 15x^2+27x-2=0 | | 8(x+2)-10=3(2x-1)+9 | | 12b-8= | | 11x-8x=156-43x | | 3-3x-2(1-x)=7(x-4)+29 | | -152-9x=8x+18 | | x-0.3x= | | 10x+15=4x+165 | | 6x+6=-59-7x | | 8x-5=4x-1 | | 2x+57=7x+12whatisx | | 173-5x=6x+8 | | 15-5x=6-8x | | 5(x-2)=10 | | m+(-8)=2 | | 2x+9=-18-7x | | b+80=-80 | | 86-4x=2x+20 | | 2x+40=11x-68 | | j+1.2=2.8 | | 5x+57=10x+12 |

Equations solver categories