7m^2-(47)m=-2

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Solution for 7m^2-(47)m=-2 equation:


Simplifying
7m2 + -1(47) * m = -2

Multiply -1 * 47
7m2 + -47m = -2

Reorder the terms:
-47m + 7m2 = -2

Solving
-47m + 7m2 = -2

Solving for variable 'm'.

Reorder the terms:
2 + -47m + 7m2 = -2 + 2

Combine like terms: -2 + 2 = 0
2 + -47m + 7m2 = 0

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

Divide each side by '7'.
0.2857142857 + -6.714285714m + m2 = 0

Move the constant term to the right:

Add '-0.2857142857' to each side of the equation.
0.2857142857 + -6.714285714m + -0.2857142857 + m2 = 0 + -0.2857142857

Reorder the terms:
0.2857142857 + -0.2857142857 + -6.714285714m + m2 = 0 + -0.2857142857

Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000
0.0000000000 + -6.714285714m + m2 = 0 + -0.2857142857
-6.714285714m + m2 = 0 + -0.2857142857

Combine like terms: 0 + -0.2857142857 = -0.2857142857
-6.714285714m + m2 = -0.2857142857

The m term is -6.714285714m.  Take half its coefficient (-3.357142857).
Square it (11.27040816) and add it to both sides.

Add '11.27040816' to each side of the equation.
-6.714285714m + 11.27040816 + m2 = -0.2857142857 + 11.27040816

Reorder the terms:
11.27040816 + -6.714285714m + m2 = -0.2857142857 + 11.27040816

Combine like terms: -0.2857142857 + 11.27040816 = 10.9846938743
11.27040816 + -6.714285714m + m2 = 10.9846938743

Factor a perfect square on the left side:
(m + -3.357142857)(m + -3.357142857) = 10.9846938743

Calculate the square root of the right side: 3.314316502

Break this problem into two subproblems by setting 
(m + -3.357142857) equal to 3.314316502 and -3.314316502.

Subproblem 1

m + -3.357142857 = 3.314316502 Simplifying m + -3.357142857 = 3.314316502 Reorder the terms: -3.357142857 + m = 3.314316502 Solving -3.357142857 + m = 3.314316502 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3.357142857' to each side of the equation. -3.357142857 + 3.357142857 + m = 3.314316502 + 3.357142857 Combine like terms: -3.357142857 + 3.357142857 = 0.000000000 0.000000000 + m = 3.314316502 + 3.357142857 m = 3.314316502 + 3.357142857 Combine like terms: 3.314316502 + 3.357142857 = 6.671459359 m = 6.671459359 Simplifying m = 6.671459359

Subproblem 2

m + -3.357142857 = -3.314316502 Simplifying m + -3.357142857 = -3.314316502 Reorder the terms: -3.357142857 + m = -3.314316502 Solving -3.357142857 + m = -3.314316502 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3.357142857' to each side of the equation. -3.357142857 + 3.357142857 + m = -3.314316502 + 3.357142857 Combine like terms: -3.357142857 + 3.357142857 = 0.000000000 0.000000000 + m = -3.314316502 + 3.357142857 m = -3.314316502 + 3.357142857 Combine like terms: -3.314316502 + 3.357142857 = 0.042826355 m = 0.042826355 Simplifying m = 0.042826355

Solution

The solution to the problem is based on the solutions from the subproblems. m = {6.671459359, 0.042826355}

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