2m^2-4m=3

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Solution for 2m^2-4m=3 equation:


Simplifying
2m2 + -4m = 3

Reorder the terms:
-4m + 2m2 = 3

Solving
-4m + 2m2 = 3

Solving for variable 'm'.

Reorder the terms:
-3 + -4m + 2m2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + -4m + 2m2 = 0

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

Divide each side by '2'.
-1.5 + -2m + m2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -2m + 1.5 + m2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -2m + m2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -2m + m2 = 0 + 1.5
-2m + m2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-2m + m2 = 1.5

The m term is -2m.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2m + 1 + m2 = 1.5 + 1

Reorder the terms:
1 + -2m + m2 = 1.5 + 1

Combine like terms: 1.5 + 1 = 2.5
1 + -2m + m2 = 2.5

Factor a perfect square on the left side:
(m + -1)(m + -1) = 2.5

Calculate the square root of the right side: 1.58113883

Break this problem into two subproblems by setting 
(m + -1) equal to 1.58113883 and -1.58113883.

Subproblem 1

m + -1 = 1.58113883 Simplifying m + -1 = 1.58113883 Reorder the terms: -1 + m = 1.58113883 Solving -1 + m = 1.58113883 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + m = 1.58113883 + 1 Combine like terms: -1 + 1 = 0 0 + m = 1.58113883 + 1 m = 1.58113883 + 1 Combine like terms: 1.58113883 + 1 = 2.58113883 m = 2.58113883 Simplifying m = 2.58113883

Subproblem 2

m + -1 = -1.58113883 Simplifying m + -1 = -1.58113883 Reorder the terms: -1 + m = -1.58113883 Solving -1 + m = -1.58113883 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + m = -1.58113883 + 1 Combine like terms: -1 + 1 = 0 0 + m = -1.58113883 + 1 m = -1.58113883 + 1 Combine like terms: -1.58113883 + 1 = -0.58113883 m = -0.58113883 Simplifying m = -0.58113883

Solution

The solution to the problem is based on the solutions from the subproblems. m = {2.58113883, -0.58113883}

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