x^2(x^2-14)+15=0

Simple and best practice solution for x^2(x^2-14)+15=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^2(x^2-14)+15=0 equation: 


Simplifying
x2(x2 + -14) + 15 = 0

Reorder the terms:
x2(-14 + x2) + 15 = 0
(-14 * x2 + x2 * x2) + 15 = 0
(-14x2 + x4) + 15 = 0

Reorder the terms:
15 + -14x2 + x4 = 0

Solving
15 + -14x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + -14x2 + -15 + x4 = 0 + -15

Reorder the terms:
15 + -15 + -14x2 + x4 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -14x2 + x4 = 0 + -15
-14x2 + x4 = 0 + -15

Combine like terms: 0 + -15 = -15
-14x2 + x4 = -15

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 = -15 + 49

Reorder the terms:
49 + -14x2 + x4 = -15 + 49

Combine like terms: -15 + 49 = 34
49 + -14x2 + x4 = 34

Factor a perfect square on the left side:
(x2 + -7)(x2 + -7) = 34

Calculate the square root of the right side: 5.830951895

Break this problem into two subproblems by setting 
(x2 + -7) equal to 5.830951895 and -5.830951895.


Subproblem 1
x2 + -7 = 5.830951895

Simplifying
x2 + -7 = 5.830951895

Reorder the terms:
-7 + x2 = 5.830951895

Solving
-7 + x2 = 5.830951895

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 = 5.830951895 + 7

Combine like terms: -7 + 7 = 0
0 + x2 = 5.830951895 + 7
x2 = 5.830951895 + 7

Combine like terms: 5.830951895 + 7 = 12.830951895
x2 = 12.830951895

Simplifying
x2 = 12.830951895

Take the square root of each side:
x = {-3.582031811, 3.582031811}


Subproblem 2
x2 + -7 = -5.830951895

Simplifying
x2 + -7 = -5.830951895

Reorder the terms:
-7 + x2 = -5.830951895

Solving
-7 + x2 = -5.830951895

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 = -5.830951895 + 7

Combine like terms: -7 + 7 = 0
0 + x2 = -5.830951895 + 7
x2 = -5.830951895 + 7

Combine like terms: -5.830951895 + 7 = 1.169048105
x2 = 1.169048105

Simplifying
x2 = 1.169048105

Take the square root of each side:
x = {-1.081225279, 1.081225279}


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.582031811, 3.582031811, -1.081225279, 1.081225279}

See similar equations:

| 9y-1=4y+14 | | 4a-4=5a-10 | | 7m+2=3m+22 | | 7.2/x=4.8 | | 234-6x=30x+20 | | 12x+4-5x+7=6-x+4+17 | | 4x+5+7x+1= | | 5h^2+5=-5 | | 3-3a=-27 | | 6a/5/2a | | 3.3-5.7x=4.7 | | 3.3-5.7=4.7 | | 10(2x-5)=5 | | 16x/12=24600 | | x^2+y^2=57 | | k-(-14)=1 | | 1/2x^2+5x=0 | | k^2-30=k | | x^3-3x^2-8x+160=0 | | 12-9x=177-44 | | 12+4y=16 | | 2y+10=3x | | 30+4y=16 | | 7x+12=84+x | | 67-4x=8x-9x | | 3y+1=27 | | 1+7x=61+8 | | 3/5-20 | | 6x-4=13-30 | | 54-2x=25x+15 | | 11x-8=52-15x | | x^2-72x+72=0 |

Equations solver categories