x^4-15x^2=-12

Simple and best practice solution for x^4-15x^2=-12 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^4-15x^2=-12 equation:


Simplifying
x4 + -15x2 = -12

Reorder the terms:
-15x2 + x4 = -12

Solving
-15x2 + x4 = -12

Solving for variable 'x'.

Reorder the terms:
12 + -15x2 + x4 = -12 + 12

Combine like terms: -12 + 12 = 0
12 + -15x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + -15x2 + -12 + x4 = 0 + -12

Reorder the terms:
12 + -12 + -15x2 + x4 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -15x2 + x4 = 0 + -12
-15x2 + x4 = 0 + -12

Combine like terms: 0 + -12 = -12
-15x2 + x4 = -12

The x term is -15x2.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15x2 + 56.25 + x4 = -12 + 56.25

Reorder the terms:
56.25 + -15x2 + x4 = -12 + 56.25

Combine like terms: -12 + 56.25 = 44.25
56.25 + -15x2 + x4 = 44.25

Factor a perfect square on the left side:
(x2 + -7.5)(x2 + -7.5) = 44.25

Calculate the square root of the right side: 6.652067348

Break this problem into two subproblems by setting 
(x2 + -7.5) equal to 6.652067348 and -6.652067348.

Subproblem 1

x2 + -7.5 = 6.652067348 Simplifying x2 + -7.5 = 6.652067348 Reorder the terms: -7.5 + x2 = 6.652067348 Solving -7.5 + x2 = 6.652067348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x2 = 6.652067348 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x2 = 6.652067348 + 7.5 x2 = 6.652067348 + 7.5 Combine like terms: 6.652067348 + 7.5 = 14.152067348 x2 = 14.152067348 Simplifying x2 = 14.152067348 Take the square root of each side: x = {-3.761923358, 3.761923358}

Subproblem 2

x2 + -7.5 = -6.652067348 Simplifying x2 + -7.5 = -6.652067348 Reorder the terms: -7.5 + x2 = -6.652067348 Solving -7.5 + x2 = -6.652067348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x2 = -6.652067348 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x2 = -6.652067348 + 7.5 x2 = -6.652067348 + 7.5 Combine like terms: -6.652067348 + 7.5 = 0.847932652 x2 = 0.847932652 Simplifying x2 = 0.847932652 Take the square root of each side: x = {-0.920832586, 0.920832586}

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-3.761923358, 3.761923358, -0.920832586, 0.920832586}

See similar equations:

| x-1=-(2x-11) | | 8-(6-6n)+20n=-14+24(n+1) | | 3(x-1)-1=3x-16 | | -(-19)=43 | | x=-(3x-8) | | 4-8x=2x+4 | | 2(x+a)=c | | 2x+3(5x-4)=5x-(-7x-18) | | 3(9s+5)-17s=2(5s+6)-13 | | 64p^3-125q^6= | | 3x^2+5=x^2+55 | | 2.9+10m=8.12 | | onehalfx=y | | (x*x)+(x*-1)+(x*x)+(x*1)= | | 5*y+4=4*y+5 | | 16p-4=4(4p+7) | | 35d+.08=25d+25 | | 2-3x(-4)=14 | | 2+6*x=1-x | | 5=-7-6x | | 16=4a | | (2)6x+4=4x+16 | | 7x+4-6=3x+2 | | 13-2(2w-1)=5w-2(5+w) | | 288=-u+6 | | 5k-37=3(1+5k) | | 65x=42.25 | | 4x+12=7x+6 | | 4x-12+5x=15 | | -2p+3=9(7p-6)-7(3+9p) | | (X+15)+X=64 | | 4m+1-m+2=20 |

Equations solver categories