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

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


Simplifying
2x2 + 3x + -1 = x2 + -2

Reorder the terms:
-1 + 3x + 2x2 = x2 + -2

Reorder the terms:
-1 + 3x + 2x2 = -2 + x2

Solving
-1 + 3x + 2x2 = -2 + x2

Solving for variable 'x'.

Reorder the terms:
-1 + 2 + 3x + 2x2 + -1x2 = -2 + x2 + 2 + -1x2

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

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

Reorder the terms:
1 + 3x + 1x2 = -2 + 2 + x2 + -1x2

Combine like terms: -2 + 2 = 0
1 + 3x + 1x2 = 0 + x2 + -1x2
1 + 3x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
1 + 3x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 3x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 3x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3x + x2 = 0 + -1
3x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
3x + x2 = -1

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 = -1 + 2.25

Reorder the terms:
2.25 + 3x + x2 = -1 + 2.25

Combine like terms: -1 + 2.25 = 1.25
2.25 + 3x + x2 = 1.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(x + 1.5) equal to 1.118033989 and -1.118033989.

Subproblem 1

x + 1.5 = 1.118033989 Simplifying x + 1.5 = 1.118033989 Reorder the terms: 1.5 + x = 1.118033989 Solving 1.5 + x = 1.118033989 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 = 1.118033989 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.118033989 + -1.5 x = 1.118033989 + -1.5 Combine like terms: 1.118033989 + -1.5 = -0.381966011 x = -0.381966011 Simplifying x = -0.381966011

Subproblem 2

x + 1.5 = -1.118033989 Simplifying x + 1.5 = -1.118033989 Reorder the terms: 1.5 + x = -1.118033989 Solving 1.5 + x = -1.118033989 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 = -1.118033989 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.118033989 + -1.5 x = -1.118033989 + -1.5 Combine like terms: -1.118033989 + -1.5 = -2.618033989 x = -2.618033989 Simplifying x = -2.618033989

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.381966011, -2.618033989}

See similar equations:

| 9-4x=57 | | 7p+15-5p-10=17+13p | | 0.1(x+5)= | | s^2-2s-15=0 | | t+5+3t=1 | | 8-3y=y | | 7x+1=19+x | | 2.2t-14.8=5.45 | | 57a-55=46a | | 6a-13=11 | | (3x+1)(6-4x)=0 | | 3p-4=3 | | -x+7x+9+x^2=7+4x^2 | | y-26=22 | | 5(2x-1)-1=8x+4 | | 6a-8=10 | | 4x*2-69x-54=0 | | 6x+1=19+x | | 3=-5+2n | | 196+36=c^2 | | 12q-15=6q+9 | | 900+324=c^2 | | 10.33-1.7y=7.67+2.1y | | 8(x-3)=-2(5-x) | | 5=1+4(x-6) | | 324+64=c^2 | | 3x+16=x | | 3(47-8)=12 | | 100-a^2=225 | | 3(a+2)=2(a-2) | | 2h^2-7h+6=0 | | 25+144=c^2 |

Equations solver categories