x^2=x+32

Simple and best practice solution for x^2=x+32 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=x+32 equation:


Simplifying
x2 = x + 32

Reorder the terms:
x2 = 32 + x

Solving
x2 = 32 + x

Solving for variable 'x'.

Reorder the terms:
-32 + -1x + x2 = 32 + x + -32 + -1x

Reorder the terms:
-32 + -1x + x2 = 32 + -32 + x + -1x

Combine like terms: 32 + -32 = 0
-32 + -1x + x2 = 0 + x + -1x
-32 + -1x + x2 = x + -1x

Combine like terms: x + -1x = 0
-32 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + -1x + 32 + x2 = 0 + 32

Reorder the terms:
-32 + 32 + -1x + x2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + -1x + x2 = 0 + 32
-1x + x2 = 0 + 32

Combine like terms: 0 + 32 = 32
-1x + x2 = 32

The x term is -1x.  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 = 32 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 32 + 0.25

Combine like terms: 32 + 0.25 = 32.25
0.25 + -1x + x2 = 32.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 32.25

Calculate the square root of the right side: 5.678908346

Break this problem into two subproblems by setting 
(x + -0.5) equal to 5.678908346 and -5.678908346.

Subproblem 1

x + -0.5 = 5.678908346 Simplifying x + -0.5 = 5.678908346 Reorder the terms: -0.5 + x = 5.678908346 Solving -0.5 + x = 5.678908346 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 = 5.678908346 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 5.678908346 + 0.5 x = 5.678908346 + 0.5 Combine like terms: 5.678908346 + 0.5 = 6.178908346 x = 6.178908346 Simplifying x = 6.178908346

Subproblem 2

x + -0.5 = -5.678908346 Simplifying x + -0.5 = -5.678908346 Reorder the terms: -0.5 + x = -5.678908346 Solving -0.5 + x = -5.678908346 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 = -5.678908346 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -5.678908346 + 0.5 x = -5.678908346 + 0.5 Combine like terms: -5.678908346 + 0.5 = -5.178908346 x = -5.178908346 Simplifying x = -5.178908346

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.178908346, -5.178908346}

See similar equations:

| 7(x+4)-3x= | | 256-9x= | | 4(3x+5)=11x+1 | | y=.05(150)+30 | | -7v-8v= | | 6y-15-5y=-24 | | 1/4(X-4)+2/5(X-5)=1/5(X^2-53) | | x+x/10=33 | | 1+10b+b-10= | | 1/4h+1/2h+1/4h+4=8 | | 6x+5+5(x+1)=4x+3 | | -6n+5n= | | 2X+5X-9= | | -80-10t=-140 | | 0.04=0.2x-8 | | 18*600= | | -5r+6r= | | X^2-y^2=97 | | 2m-6+3m= | | 12a+18b=180 | | 4(3)+5(-1.2)= | | 4(3)+5(-12)= | | 0.183x^2+0.015x-0.458=0 | | 0.50x+0.10(30)=0.25(84) | | 8+3n+6= | | 4.5+x=7 | | (-5)(-2)(7)= | | 5-3(-7)= | | 5y-3y=-30 | | 7w=4w+21 | | -3n-9n= | | 1-p+p+1= |

Equations solver categories