10m^2-2m=3

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Solution for 10m^2-2m=3 equation:


Simplifying
10m2 + -2m = 3

Reorder the terms:
-2m + 10m2 = 3

Solving
-2m + 10m2 = 3

Solving for variable 'm'.

Reorder the terms:
-3 + -2m + 10m2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + -2m + 10m2 = 0

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

Divide each side by '10'.
-0.3 + -0.2m + m2 = 0

Move the constant term to the right:

Add '0.3' to each side of the equation.
-0.3 + -0.2m + 0.3 + m2 = 0 + 0.3

Reorder the terms:
-0.3 + 0.3 + -0.2m + m2 = 0 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + -0.2m + m2 = 0 + 0.3
-0.2m + m2 = 0 + 0.3

Combine like terms: 0 + 0.3 = 0.3
-0.2m + m2 = 0.3

The m term is -0.2m.  Take half its coefficient (-0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
-0.2m + 0.01 + m2 = 0.3 + 0.01

Reorder the terms:
0.01 + -0.2m + m2 = 0.3 + 0.01

Combine like terms: 0.3 + 0.01 = 0.31
0.01 + -0.2m + m2 = 0.31

Factor a perfect square on the left side:
(m + -0.1)(m + -0.1) = 0.31

Calculate the square root of the right side: 0.556776436

Break this problem into two subproblems by setting 
(m + -0.1) equal to 0.556776436 and -0.556776436.

Subproblem 1

m + -0.1 = 0.556776436 Simplifying m + -0.1 = 0.556776436 Reorder the terms: -0.1 + m = 0.556776436 Solving -0.1 + m = 0.556776436 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + m = 0.556776436 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + m = 0.556776436 + 0.1 m = 0.556776436 + 0.1 Combine like terms: 0.556776436 + 0.1 = 0.656776436 m = 0.656776436 Simplifying m = 0.656776436

Subproblem 2

m + -0.1 = -0.556776436 Simplifying m + -0.1 = -0.556776436 Reorder the terms: -0.1 + m = -0.556776436 Solving -0.1 + m = -0.556776436 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + m = -0.556776436 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + m = -0.556776436 + 0.1 m = -0.556776436 + 0.1 Combine like terms: -0.556776436 + 0.1 = -0.456776436 m = -0.456776436 Simplifying m = -0.456776436

Solution

The solution to the problem is based on the solutions from the subproblems. m = {0.656776436, -0.456776436}

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