81-x^2=2+x

Simple and best practice solution for 81-x^2=2+x 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 81-x^2=2+x equation:


Simplifying
81 + -1x2 = 2 + x

Solving
81 + -1x2 = 2 + x

Solving for variable 'x'.

Reorder the terms:
81 + -2 + -1x + -1x2 = 2 + x + -2 + -1x

Combine like terms: 81 + -2 = 79
79 + -1x + -1x2 = 2 + x + -2 + -1x

Reorder the terms:
79 + -1x + -1x2 = 2 + -2 + x + -1x

Combine like terms: 2 + -2 = 0
79 + -1x + -1x2 = 0 + x + -1x
79 + -1x + -1x2 = x + -1x

Combine like terms: x + -1x = 0
79 + -1x + -1x2 = 0

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

Divide each side by '-1'.
-79 + x + x2 = 0

Move the constant term to the right:

Add '79' to each side of the equation.
-79 + x + 79 + x2 = 0 + 79

Reorder the terms:
-79 + 79 + x + x2 = 0 + 79

Combine like terms: -79 + 79 = 0
0 + x + x2 = 0 + 79
x + x2 = 0 + 79

Combine like terms: 0 + 79 = 79
x + x2 = 79

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.
 + 0.25 + x2 = 79 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 79 + 0.25

Combine like terms: 79 + 0.25 = 79.25
1.25 + x2 = 79.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 79.25

Calculate the square root of the right side: 8.902246907

Break this problem into two subproblems by setting 
(x + 0.5) equal to 8.902246907 and -8.902246907.

Subproblem 1

x + 0.5 = 8.902246907 Simplifying x + 0.5 = 8.902246907 Reorder the terms: 0.5 + x = 8.902246907 Solving 0.5 + x = 8.902246907 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 = 8.902246907 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 8.902246907 + -0.5 x = 8.902246907 + -0.5 Combine like terms: 8.902246907 + -0.5 = 8.402246907 x = 8.402246907 Simplifying x = 8.402246907

Subproblem 2

x + 0.5 = -8.902246907 Simplifying x + 0.5 = -8.902246907 Reorder the terms: 0.5 + x = -8.902246907 Solving 0.5 + x = -8.902246907 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 = -8.902246907 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -8.902246907 + -0.5 x = -8.902246907 + -0.5 Combine like terms: -8.902246907 + -0.5 = -9.402246907 x = -9.402246907 Simplifying x = -9.402246907

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.402246907, -9.402246907}

See similar equations:

| 6(3h-2y)= | | 1x/3x+10=55 | | G=5/4(p-83) | | 85r-87r=70 | | 3x-b=9 | | x+4x=-10 | | -13+n=-8 | | 5000(x+10000)=12+1 | | -19-m=-4m+4(1-5m) | | 3(-6x+9)-10x= | | 7x+5x+-20x+9=1 | | -2(w-7)+10w=-34 | | 7x+-5x+-20x+9=1 | | -6(-12r-11)=-6(1-10r) | | (18-16)/2*2+4 | | 5-216-18+9= | | -0.5t-3t+5=0 | | 3/8-1/4t=1/2t-1/3 | | 1/2(r+6.5) | | 3(y-6)+6=5y-6 | | 10(-3+x)-2(x-12)=5x+9x | | 7Y(6y+3)= | | 20/24x3/4 | | 11t+-18t+17t+-6t=-20 | | 2(x-3)-17=3(x+2) | | -6w+8=-6-(-8) | | 2(6+b)=32+7b | | -3(p-6)=-6(p-2)-3p | | 6(-10+7x)=360 | | -5=n+3 | | (2x-4)=(4x-5) | | 37/12+8/9 |

Equations solver categories