x^2+4x+7=180

Simple and best practice solution for x^2+4x+7=180 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+4x+7=180 equation: 


Simplifying
x2 + 4x + 7 = 180

Reorder the terms:
7 + 4x + x2 = 180

Solving
7 + 4x + x2 = 180

Solving for variable 'x'.

Reorder the terms:
7 + -180 + 4x + x2 = 180 + -180

Combine like terms: 7 + -180 = -173
-173 + 4x + x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-173 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '173' to each side of the equation.
-173 + 4x + 173 + x2 = 0 + 173

Reorder the terms:
-173 + 173 + 4x + x2 = 0 + 173

Combine like terms: -173 + 173 = 0
0 + 4x + x2 = 0 + 173
4x + x2 = 0 + 173

Combine like terms: 0 + 173 = 173
4x + x2 = 173

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 173 + 4

Reorder the terms:
4 + 4x + x2 = 173 + 4

Combine like terms: 173 + 4 = 177
4 + 4x + x2 = 177

Factor a perfect square on the left side:
(x + 2)(x + 2) = 177

Calculate the square root of the right side: 13.304134696

Break this problem into two subproblems by setting 
(x + 2) equal to 13.304134696 and -13.304134696.


Subproblem 1
x + 2 = 13.304134696

Simplifying
x + 2 = 13.304134696

Reorder the terms:
2 + x = 13.304134696

Solving
2 + x = 13.304134696

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + x = 13.304134696 + -2

Combine like terms: 2 + -2 = 0
0 + x = 13.304134696 + -2
x = 13.304134696 + -2

Combine like terms: 13.304134696 + -2 = 11.304134696
x = 11.304134696

Simplifying
x = 11.304134696


Subproblem 2
x + 2 = -13.304134696

Simplifying
x + 2 = -13.304134696

Reorder the terms:
2 + x = -13.304134696

Solving
2 + x = -13.304134696

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + x = -13.304134696 + -2

Combine like terms: 2 + -2 = 0
0 + x = -13.304134696 + -2
x = -13.304134696 + -2

Combine like terms: -13.304134696 + -2 = -15.304134696
x = -15.304134696

Simplifying
x = -15.304134696


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.304134696, -15.304134696}

See similar equations:

| 7x-18=-74 | | -1+6x=-37 | | 1R=1V/1I | | 5am+2b-b+4a= | | -1+2+(-8)= | | q^3-8=0 | | 22-3a=4a+1 | | 3x+2y-1=4 | | 23-3a=4a+1 | | 20+x=2 | | 22=58-x | | X-33=19 | | (1)/sqrt(14) | | 2k+3.4=k+6 | | 4x-36y=16 | | sin(7x)=sin(x) | | 2k+4.2=k+12 | | y=4xyz | | 16=55-x | | (C^4+2C^2D^2-D^4)(2C-2CD+D)= | | X-30=15 | | 12-1/3w=2 | | w^2+3w-130=0 | | 3q^2-17q-28=0 | | 28+x=9 | | 3q^2-17q-28q=0 | | -y^2+17y-42=0 | | -14A+8+19A=43 | | 3x^12=132 | | E+(E+54)=180 | | x^12=132 | | 4/x=16/5 |

Equations solver categories