3x^2-5x-1=x^2+x

Simple and best practice solution for 3x^2-5x-1=x^2+x 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 3x^2-5x-1=x^2+x equation:


Simplifying
3x2 + -5x + -1 = x2 + x

Reorder the terms:
-1 + -5x + 3x2 = x2 + x

Reorder the terms:
-1 + -5x + 3x2 = x + x2

Solving
-1 + -5x + 3x2 = x + x2

Solving for variable 'x'.

Reorder the terms:
-1 + -5x + -1x + 3x2 + -1x2 = x + x2 + -1x + -1x2

Combine like terms: -5x + -1x = -6x
-1 + -6x + 3x2 + -1x2 = x + x2 + -1x + -1x2

Combine like terms: 3x2 + -1x2 = 2x2
-1 + -6x + 2x2 = x + x2 + -1x + -1x2

Reorder the terms:
-1 + -6x + 2x2 = x + -1x + x2 + -1x2

Combine like terms: x + -1x = 0
-1 + -6x + 2x2 = 0 + x2 + -1x2
-1 + -6x + 2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-1 + -6x + 2x2 = 0

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

Divide each side by '2'.
-0.5 + -3x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -3x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -3x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -3x + x2 = 0 + 0.5
-3x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-3x + x2 = 0.5

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 0.5 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 0.5 + 2.25

Combine like terms: 0.5 + 2.25 = 2.75
2.25 + -3x + x2 = 2.75

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 2.75

Calculate the square root of the right side: 1.658312395

Break this problem into two subproblems by setting 
(x + -1.5) equal to 1.658312395 and -1.658312395.

Subproblem 1

x + -1.5 = 1.658312395 Simplifying x + -1.5 = 1.658312395 Reorder the terms: -1.5 + x = 1.658312395 Solving -1.5 + x = 1.658312395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.658312395 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.658312395 + 1.5 x = 1.658312395 + 1.5 Combine like terms: 1.658312395 + 1.5 = 3.158312395 x = 3.158312395 Simplifying x = 3.158312395

Subproblem 2

x + -1.5 = -1.658312395 Simplifying x + -1.5 = -1.658312395 Reorder the terms: -1.5 + x = -1.658312395 Solving -1.5 + x = -1.658312395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.658312395 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.658312395 + 1.5 x = -1.658312395 + 1.5 Combine like terms: -1.658312395 + 1.5 = -0.158312395 x = -0.158312395 Simplifying x = -0.158312395

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.158312395, -0.158312395}

See similar equations:

| 12x-100=30+7x | | ln(x-8)=3 | | 7e-4=13 | | -10y+108=72-36y | | 3-x/6=4x+1/4 | | n^2-5n=-8 | | 4x^3-144x^2+1152x=0 | | 7m+n=2 | | 4a+6b-4b= | | 5c-4=6-(2+6c) | | 4x=6x+(-14) | | 5(4x+8)= | | 3x+2/5=x-7/2 | | 5-3z+3(3-5z)=12 | | (7-6t)-(4-7t)=-3 | | 2x^2-12=-5xfactor | | 4x-1=2x/3 | | 1+3q=13 | | -9x-119=3x+109 | | x^2+2819-x^2+6296+4= | | x^2+2819-x^2+6296= | | 6(3x-2)=2(10+x) | | 7x^2+52+60=0 | | 2k^2-7k-4=0 | | 9=21x^2 | | 2a=-6-64 | | -5x-77=70+2x | | 9=21x | | x^2+6296*2819+2819= | | 7n^2-32n+20=0 | | 8(x+1)=-3x+52 | | x^2+6296*2819-2819= |

Equations solver categories