x+7=x^2

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


Simplifying
x + 7 = x2

Reorder the terms:
7 + x = x2

Solving
7 + x = x2

Solving for variable 'x'.

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

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

Divide each side by '-1'.
-7 + -1x + x2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -1x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + -1x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x + x2 = 0 + 7
-1x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-1x + x2 = 7

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 7 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 7 + 0.25

Combine like terms: 7 + 0.25 = 7.25
0.25 + -1x + x2 = 7.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(x + 0.5) equal to 2.692582404 and -2.692582404.

Subproblem 1

x + 0.5 = 2.692582404 Simplifying x + 0.5 = 2.692582404 Reorder the terms: 0.5 + x = 2.692582404 Solving 0.5 + x = 2.692582404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.692582404 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.692582404 + -0.5 x = 2.692582404 + -0.5 Combine like terms: 2.692582404 + -0.5 = 2.192582404 x = 2.192582404 Simplifying x = 2.192582404

Subproblem 2

x + 0.5 = -2.692582404 Simplifying x + 0.5 = -2.692582404 Reorder the terms: 0.5 + x = -2.692582404 Solving 0.5 + x = -2.692582404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.692582404 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.692582404 + -0.5 x = -2.692582404 + -0.5 Combine like terms: -2.692582404 + -0.5 = -3.192582404 x = -3.192582404 Simplifying x = -3.192582404

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.192582404, -3.192582404}

See similar equations:

| -19-3+28-40=-4-3m-6+4m | | -36(13x)+28(19x)= | | 10r=30 | | 9.2-p=6.8 | | -16=-2m | | 4x^2-27=x^2 | | -5(t+7)=0 | | 5y^2-2y^3-7y^2+7y^3= | | 4m+16=0 | | 0=20-4m | | 12=4x-2-2(x+2) | | 30-x-x^2= | | 4(c-2)+5=2+c-5 | | -5-3=8-3x+4x | | t=ud^2 | | 14(x+10)+6=7x+(223) | | 3(3x-5)-2(4x-3)=5-10 | | 4x^2+23x-6= | | -6(3p+3)-40=4(2p+5) | | 5=5p-10 | | 4+7n=9n^2 | | 7-6n+4n=28-71 | | X=0.6x+386 | | 9-2a=5 | | 5x-(4x+8)=2x-29 | | 2x+2y=96 | | .22y-2.2=.12y+1-.7y | | 4n-12=-12+5n | | 4(c-2)+6=5+c-7 | | 5x-(3x-8)=26 | | .5x=6+.6x | | 30x^2-10=0 |

Equations solver categories