x^2+x-5=3

Simple and best practice solution for x^2+x-5=3 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-5=3 equation:


Simplifying
x2 + x + -5 = 3

Reorder the terms:
-5 + x + x2 = 3

Solving
-5 + x + x2 = 3

Solving for variable 'x'.

Reorder the terms:
-5 + -3 + x + x2 = 3 + -3

Combine like terms: -5 + -3 = -8
-8 + x + x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-8 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + x + x2 = 0 + 8
x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
x + x2 = 8

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.
x + 0.25 + x2 = 8 + 0.25

Reorder the terms:
0.25 + x + x2 = 8 + 0.25

Combine like terms: 8 + 0.25 = 8.25
0.25 + x + x2 = 8.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(x + 0.5) equal to 2.872281323 and -2.872281323.


Subproblem 1
x + 0.5 = 2.872281323

Simplifying
x + 0.5 = 2.872281323

Reorder the terms:
0.5 + x = 2.872281323

Solving
0.5 + x = 2.872281323

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 = 2.872281323 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 2.872281323 + -0.5
x = 2.872281323 + -0.5

Combine like terms: 2.872281323 + -0.5 = 2.372281323
x = 2.372281323

Simplifying
x = 2.372281323


Subproblem 2
x + 0.5 = -2.872281323

Simplifying
x + 0.5 = -2.872281323

Reorder the terms:
0.5 + x = -2.872281323

Solving
0.5 + x = -2.872281323

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 = -2.872281323 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -2.872281323 + -0.5
x = -2.872281323 + -0.5

Combine like terms: -2.872281323 + -0.5 = -3.372281323
x = -3.372281323

Simplifying
x = -3.372281323


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.372281323, -3.372281323}

See similar equations:

| 4a+2b=110 | | =10x+9 | | 2x+2=x-2 | | 8X^2-80=0 | | (3x)2-27= | | 9-3y-11y=12y-8 | | w=2w^2+1 | | 2t=60-t | | 2x^2+3x-180=0 | | x-29+3x=-6x-22-3x | | 3(7b-2)=-69 | | 2x+10=7x-11 | | 4k+39=7k+6 | | 4x+3y=73 | | x=20+4y | | 10X^5*Y^4*5X^3*Y^2=0 | | 10X^5*Y^4=0 | | 48x-16=0 | | y-10.2=-6.5+7.8 | | x^2+2*x=12 | | -4x^2+6x+40=0 | | 4-10-6x+7x-9x=-12x | | (8y^2-7y+8)-(9y^2-7y+6)= | | y^2+16y-63= | | 1.2=x+(.7)(x-0) | | 1.2=x+(5)(x-2) | | 64x^2-80x+25=0 | | 64x^2-80+25=0 | | -(x+1.2)(x+0.5)=0 | | y-1564=1256 | | 900+d=1822 | | 4x+2y=60 |

Equations solver categories