3x+11=x^2-1

Simple and best practice solution for 3x+11=x^2-1 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+11=x^2-1 equation:


Simplifying
3x + 11 = x2 + -1

Reorder the terms:
11 + 3x = x2 + -1

Reorder the terms:
11 + 3x = -1 + x2

Solving
11 + 3x = -1 + x2

Solving for variable 'x'.

Reorder the terms:
11 + 1 + 3x + -1x2 = -1 + x2 + 1 + -1x2

Combine like terms: 11 + 1 = 12
12 + 3x + -1x2 = -1 + x2 + 1 + -1x2

Reorder the terms:
12 + 3x + -1x2 = -1 + 1 + x2 + -1x2

Combine like terms: -1 + 1 = 0
12 + 3x + -1x2 = 0 + x2 + -1x2
12 + 3x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
12 + 3x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-12 + -3x + x2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -3x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + -3x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -3x + x2 = 0 + 12
-3x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
-3x + x2 = 12

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 = 12 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 12 + 2.25

Combine like terms: 12 + 2.25 = 14.25
2.25 + -3x + x2 = 14.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(x + -1.5) equal to 3.774917218 and -3.774917218.

Subproblem 1

x + -1.5 = 3.774917218 Simplifying x + -1.5 = 3.774917218 Reorder the terms: -1.5 + x = 3.774917218 Solving -1.5 + x = 3.774917218 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 = 3.774917218 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 3.774917218 + 1.5 x = 3.774917218 + 1.5 Combine like terms: 3.774917218 + 1.5 = 5.274917218 x = 5.274917218 Simplifying x = 5.274917218

Subproblem 2

x + -1.5 = -3.774917218 Simplifying x + -1.5 = -3.774917218 Reorder the terms: -1.5 + x = -3.774917218 Solving -1.5 + x = -3.774917218 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 = -3.774917218 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -3.774917218 + 1.5 x = -3.774917218 + 1.5 Combine like terms: -3.774917218 + 1.5 = -2.274917218 x = -2.274917218 Simplifying x = -2.274917218

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.274917218, -2.274917218}

See similar equations:

| W+3=2w-7 | | 5x+3x-2=22 | | .04g=.252 | | 1=(-2)-f | | 13x+5.5=90 | | 9t-4t^2=0 | | 9.9t-4.9t^2=0 | | x+9+15=18 | | 23=2x+7 | | z+3/2=4 | | 36=2x+4 | | 2-y/6=6(y=2)/5 | | 5(x+8)-3= | | 5a^2b^3-45ab+15a=0 | | X-(-9)=-1 | | 2x(8x-7)=4 | | 3x+8=-27-4x | | D=wc | | -1(x-4)-2x-(-2x)-(-(-3))+1=2(-x+2) | | 647/12 | | y/5^2=100 | | 5(x+8)+8=8x-3(x-6) | | 6x=-3+42 | | 23-5x=9-7x | | 7/6x-2/3=4 | | x-5=13-x | | 647/1200=x/100 | | (8-3i)-(-6+4i)=0 | | -2m+6=5m | | 2(x+8)=8x+2-6x+14 | | 9y+8=8y-2 | | (1+i)z^2+2iz-9-3i=0 |

Equations solver categories