m^2+m=100

Simple and best practice solution for m^2+m=100 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 m^2+m=100 equation:


Simplifying
m2 + m = 100

Reorder the terms:
m + m2 = 100

Solving
m + m2 = 100

Solving for variable 'm'.

Reorder the terms:
-100 + m + m2 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + m + 100 + m2 = 0 + 100

Reorder the terms:
-100 + 100 + m + m2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + m + m2 = 0 + 100
m + m2 = 0 + 100

Combine like terms: 0 + 100 = 100
m + m2 = 100

The m term is m.  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.
m + 0.25 + m2 = 100 + 0.25

Reorder the terms:
0.25 + m + m2 = 100 + 0.25

Combine like terms: 100 + 0.25 = 100.25
0.25 + m + m2 = 100.25

Factor a perfect square on the left side:
(m + 0.5)(m + 0.5) = 100.25

Calculate the square root of the right side: 10.012492197

Break this problem into two subproblems by setting 
(m + 0.5) equal to 10.012492197 and -10.012492197.

Subproblem 1

m + 0.5 = 10.012492197 Simplifying m + 0.5 = 10.012492197 Reorder the terms: 0.5 + m = 10.012492197 Solving 0.5 + m = 10.012492197 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = 10.012492197 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = 10.012492197 + -0.5 m = 10.012492197 + -0.5 Combine like terms: 10.012492197 + -0.5 = 9.512492197 m = 9.512492197 Simplifying m = 9.512492197

Subproblem 2

m + 0.5 = -10.012492197 Simplifying m + 0.5 = -10.012492197 Reorder the terms: 0.5 + m = -10.012492197 Solving 0.5 + m = -10.012492197 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = -10.012492197 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = -10.012492197 + -0.5 m = -10.012492197 + -0.5 Combine like terms: -10.012492197 + -0.5 = -10.512492197 m = -10.512492197 Simplifying m = -10.512492197

Solution

The solution to the problem is based on the solutions from the subproblems. m = {9.512492197, -10.512492197}

See similar equations:

| 1/2x-7/6=53/6-1/3x | | 0.9x-1.1=0.3+0.2x | | 2/3x=1/6x+2 | | 5t^2=5 | | 2/3(x+3)=5/4x+17/12 | | 12(7+5y/2)^2-5y=72 | | 1/2(x-2)=2/3x-6 | | 2x^2+7=20.52 | | 40-4x=50+23 | | 5x-6=(2x-3) | | 9(x-2)=-6(4-x)+8 | | -2.9x=31.2 | | 4+(x-3)=5-7 | | 1=10+3x | | 8(3x-5)-4(2x+3)=12 | | 25=4x-3 | | X+x/4=15 | | 5=15+2x | | 8=4x-2 | | 6xy-9yx+4xy= | | 5x*5y=32 | | a+5+2a-2= | | 5p-8=3(4-p) | | 17x^3-2x^2-20x+8=0 | | 4x-5x+y+6y= | | 5(x+2)=7 | | 10x+6=7x | | 8mn+2mn-6mn= | | pq-8pq+9pq= | | 92748727x=835295 | | 6ab-5ab= | | 3x^2+10=P |

Equations solver categories