2m^2-14m=-23

Simple and best practice solution for 2m^2-14m=-23 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 2m^2-14m=-23 equation:


Simplifying
2m2 + -14m = -23

Reorder the terms:
-14m + 2m2 = -23

Solving
-14m + 2m2 = -23

Solving for variable 'm'.

Reorder the terms:
23 + -14m + 2m2 = -23 + 23

Combine like terms: -23 + 23 = 0
23 + -14m + 2m2 = 0

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

Divide each side by '2'.
11.5 + -7m + m2 = 0

Move the constant term to the right:

Add '-11.5' to each side of the equation.
11.5 + -7m + -11.5 + m2 = 0 + -11.5

Reorder the terms:
11.5 + -11.5 + -7m + m2 = 0 + -11.5

Combine like terms: 11.5 + -11.5 = 0.0
0.0 + -7m + m2 = 0 + -11.5
-7m + m2 = 0 + -11.5

Combine like terms: 0 + -11.5 = -11.5
-7m + m2 = -11.5

The m term is -7m.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7m + 12.25 + m2 = -11.5 + 12.25

Reorder the terms:
12.25 + -7m + m2 = -11.5 + 12.25

Combine like terms: -11.5 + 12.25 = 0.75
12.25 + -7m + m2 = 0.75

Factor a perfect square on the left side:
(m + -3.5)(m + -3.5) = 0.75

Calculate the square root of the right side: 0.866025404

Break this problem into two subproblems by setting 
(m + -3.5) equal to 0.866025404 and -0.866025404.

Subproblem 1

m + -3.5 = 0.866025404 Simplifying m + -3.5 = 0.866025404 Reorder the terms: -3.5 + m = 0.866025404 Solving -3.5 + m = 0.866025404 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + m = 0.866025404 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + m = 0.866025404 + 3.5 m = 0.866025404 + 3.5 Combine like terms: 0.866025404 + 3.5 = 4.366025404 m = 4.366025404 Simplifying m = 4.366025404

Subproblem 2

m + -3.5 = -0.866025404 Simplifying m + -3.5 = -0.866025404 Reorder the terms: -3.5 + m = -0.866025404 Solving -3.5 + m = -0.866025404 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + m = -0.866025404 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + m = -0.866025404 + 3.5 m = -0.866025404 + 3.5 Combine like terms: -0.866025404 + 3.5 = 2.633974596 m = 2.633974596 Simplifying m = 2.633974596

Solution

The solution to the problem is based on the solutions from the subproblems. m = {4.366025404, 2.633974596}

See similar equations:

| -(3x)/(8)=-(15)/(32) | | y=4.9t^2+49t | | B^8=40 | | 3[x-3]=30 | | y=ln(sin^4x) | | 1/3h=1 | | A(7)=615.75 | | -5y-3=-8-3y | | 1.6q-8.3q+1.2=-25.6 | | -1/5=x=2/5 | | O(10)=2(10)-1 | | 9x^4-25y^2=0 | | 6-7(4m-5)=-99 | | 2x+39+6x-9=180 | | 5-(-2x+3)=-1(1-x) | | 0.16x=15.00+0.12x | | 2x-4(-5x+2)= | | -6x^4-54x=0 | | (4x-5)+55=180 | | 53.98+0.10x=49.98+0.14x | | 6-9x=7x-9x-36 | | 3.7g+6=1.7g+16 | | 25.00-0.21x=14.71 | | 15.2/.1 | | 3.7+6=1.7g+16 | | 7=3-3(x+4) | | 12y+13=121 | | 39150+11.00x=24.50 | | r^2-10r=-21 | | (x-4/10)=(3/2) | | 14x-5=11x-2 | | 1.6a-8.3a+1.2=25.6 |

Equations solver categories