2x^2+x-24+2x^2+4=0

Simple and best practice solution for 2x^2+x-24+2x^2+4=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 2x^2+x-24+2x^2+4=0 equation:


Simplifying
2x2 + x + -24 + 2x2 + 4 = 0

Reorder the terms:
-24 + 4 + x + 2x2 + 2x2 = 0

Combine like terms: -24 + 4 = -20
-20 + x + 2x2 + 2x2 = 0

Combine like terms: 2x2 + 2x2 = 4x2
-20 + x + 4x2 = 0

Solving
-20 + x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-5 + 0.25x + x2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 0.25x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + 0.25x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 0.25x + x2 = 0 + 5
0.25x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
0.25x + x2 = 5

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.25x + 0.25 + x2 = 5 + 0.25

Reorder the terms:
0.25 + 0.25x + x2 = 5 + 0.25

Combine like terms: 5 + 0.25 = 5.25
0.25 + 0.25x + x2 = 5.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(x + 0.5) equal to 2.291287847 and -2.291287847.

Subproblem 1

x + 0.5 = 2.291287847 Simplifying x + 0.5 = 2.291287847 Reorder the terms: 0.5 + x = 2.291287847 Solving 0.5 + x = 2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.291287847 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.291287847 + -0.5 x = 2.291287847 + -0.5 Combine like terms: 2.291287847 + -0.5 = 1.791287847 x = 1.791287847 Simplifying x = 1.791287847

Subproblem 2

x + 0.5 = -2.291287847 Simplifying x + 0.5 = -2.291287847 Reorder the terms: 0.5 + x = -2.291287847 Solving 0.5 + x = -2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.291287847 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.291287847 + -0.5 x = -2.291287847 + -0.5 Combine like terms: -2.291287847 + -0.5 = -2.791287847 x = -2.791287847 Simplifying x = -2.791287847

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.791287847, -2.791287847}

See similar equations:

| 4v^2+5=-9v | | 9y^2+30y=-25 | | (x-1)(3x+1)=0 | | -11w-6=4w^2 | | 5u^2=-u+4 | | 21x^2-20x=0 | | m^2=7m | | y^2-6y+9=0 | | w^2-6w-7=0 | | 7x+3=55 | | w^2+9w+14=0 | | (4v+5)(6+v)=0 | | 4(y-6)(-y+8)=0 | | (9+w)(5w-4)=0 | | -3*-8= | | -20*-1= | | 20*-1= | | -143=-11 | | 18x^2-13x=0 | | 10x=7.5 | | x(4x-7)(x+3)= | | 2x+3y+6z-37=35x | | -4+36= | | -6+-12= | | -12+-6= | | -12+-6+-6= | | -18+1= | | -b+2=-5 | | 1.3x=9 | | -1*6t= | | -t*4t= | | 1.3x=4.5 |

Equations solver categories