x^4-14x^2+47=0

Simple and best practice solution for x^4-14x^2+47=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 x^4-14x^2+47=0 equation:


Simplifying
x4 + -14x2 + 47 = 0

Reorder the terms:
47 + -14x2 + x4 = 0

Solving
47 + -14x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-47' to each side of the equation.
47 + -14x2 + -47 + x4 = 0 + -47

Reorder the terms:
47 + -47 + -14x2 + x4 = 0 + -47

Combine like terms: 47 + -47 = 0
0 + -14x2 + x4 = 0 + -47
-14x2 + x4 = 0 + -47

Combine like terms: 0 + -47 = -47
-14x2 + x4 = -47

The x term is -14x2.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x2 + 49 + x4 = -47 + 49

Reorder the terms:
49 + -14x2 + x4 = -47 + 49

Combine like terms: -47 + 49 = 2
49 + -14x2 + x4 = 2

Factor a perfect square on the left side:
(x2 + -7)(x2 + -7) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(x2 + -7) equal to 1.414213562 and -1.414213562.

Subproblem 1

x2 + -7 = 1.414213562 Simplifying x2 + -7 = 1.414213562 Reorder the terms: -7 + x2 = 1.414213562 Solving -7 + x2 = 1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x2 = 1.414213562 + 7 Combine like terms: -7 + 7 = 0 0 + x2 = 1.414213562 + 7 x2 = 1.414213562 + 7 Combine like terms: 1.414213562 + 7 = 8.414213562 x2 = 8.414213562 Simplifying x2 = 8.414213562 Take the square root of each side: x = {-2.900726385, 2.900726385}

Subproblem 2

x2 + -7 = -1.414213562 Simplifying x2 + -7 = -1.414213562 Reorder the terms: -7 + x2 = -1.414213562 Solving -7 + x2 = -1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x2 = -1.414213562 + 7 Combine like terms: -7 + 7 = 0 0 + x2 = -1.414213562 + 7 x2 = -1.414213562 + 7 Combine like terms: -1.414213562 + 7 = 5.585786438 x2 = 5.585786438 Simplifying x2 = 5.585786438 Take the square root of each side: x = {-2.363426842, 2.363426842}

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-2.900726385, 2.900726385, -2.363426842, 2.363426842}

See similar equations:

| 3(2x-5)=2z+13 | | 2x+30=7x+15 | | 8x=0.587 | | 5-8n=-(1+2n) | | -3x^2+16x+16=0 | | 4x+1=29 | | -5=t-7 | | 2x^2-13x=-15 | | -(m+5n-13)= | | 4b+b= | | -3x^2+14x+16=0 | | 2x-1+3x+2=7x+3-5x+7 | | 2(x+3)=8-3(x-4) | | A^2+4a-32=0 | | 7x-2(4-3x)=-3(2x+1) | | (2y-3)=29 | | 13-2v=-4(v-1)-5 | | -(2-3x)= | | -(2)= | | (1/2)x+4=(-2/3)x+1/2 | | 4x+-3=4 | | 2x-18=9x+34 | | 5x-5=6x-2 | | 24s^2+30s^2b-9s^2b^2= | | 3x-5x-3=10-19 | | s=c+cx | | s^2(24s^2+30b-9b^2)= | | 5x-5=4x-9 | | (-5)(3x-7)=(3)(3x+1) | | -12n-4(n-3)=-12(n+5)+8 | | 4n-5(n-3)=3(n+1)-4 | | 6x-3x+2=8 |

Equations solver categories