-x^2+4=(3x-1)2

Simple and best practice solution for -x^2+4=(3x-1)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 -x^2+4=(3x-1)2 equation:


Simplifying
-1x2 + 4 = (3x + -1) * 2

Reorder the terms:
4 + -1x2 = (3x + -1) * 2

Reorder the terms:
4 + -1x2 = (-1 + 3x) * 2

Reorder the terms for easier multiplication:
4 + -1x2 = 2(-1 + 3x)
4 + -1x2 = (-1 * 2 + 3x * 2)
4 + -1x2 = (-2 + 6x)

Solving
4 + -1x2 = -2 + 6x

Solving for variable 'x'.

Reorder the terms:
4 + 2 + -6x + -1x2 = -2 + 6x + 2 + -6x

Combine like terms: 4 + 2 = 6
6 + -6x + -1x2 = -2 + 6x + 2 + -6x

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

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

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

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

Divide each side by '-1'.
-6 + 6x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 6x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + 6x + x2 = 0 + 6

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

Combine like terms: 0 + 6 = 6
6x + x2 = 6

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 6 + 9

Reorder the terms:
9 + 6x + x2 = 6 + 9

Combine like terms: 6 + 9 = 15
9 + 6x + x2 = 15

Factor a perfect square on the left side:
(x + 3)(x + 3) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(x + 3) equal to 3.872983346 and -3.872983346.

Subproblem 1

x + 3 = 3.872983346 Simplifying x + 3 = 3.872983346 Reorder the terms: 3 + x = 3.872983346 Solving 3 + x = 3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 3.872983346 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.872983346 + -3 x = 3.872983346 + -3 Combine like terms: 3.872983346 + -3 = 0.872983346 x = 0.872983346 Simplifying x = 0.872983346

Subproblem 2

x + 3 = -3.872983346 Simplifying x + 3 = -3.872983346 Reorder the terms: 3 + x = -3.872983346 Solving 3 + x = -3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -3.872983346 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.872983346 + -3 x = -3.872983346 + -3 Combine like terms: -3.872983346 + -3 = -6.872983346 x = -6.872983346 Simplifying x = -6.872983346

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.872983346, -6.872983346}

See similar equations:

| 3e=-24 | | 3e=-25 | | 10x-17=0 | | d+-16=-15 | | c+8=1 | | 2x^2+14x=-9 | | 5b=-20 | | -4y^2-y=-10 | | x^2+8x-27=0 | | 100*y=1.1058 | | 4.1*q=34.85 | | 8a-12=15a-4 | | 4a^4b^2+a^2b=0 | | 11y^4+7y^4=0 | | x+01=6 | | 1+3x=-3+4x | | 4(3x-8)=2(6x+6) | | 8+2x-5=6x+7-2x | | 158-5x=22x+20 | | 2x^2-8x=Pr | | 5+16-3(7)+9=-1 | | 12x-5=127 | | 12x+5=127 | | 16x+6x=100 | | log^2(x+6)+log^2+3=log^2+30 | | 3x-6y=2 | | log^2(x+6)+log^2+3=log^230 | | 2x^2-14x+23=0 | | -7=3x+8 | | 18x^2-9x+1=0 | | 2r+17r=76 | | .66+w=1.5 |

Equations solver categories