8m^2+2m=11

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Solution for 8m^2+2m=11 equation:


Simplifying
8m2 + 2m = 11

Reorder the terms:
2m + 8m2 = 11

Solving
2m + 8m2 = 11

Solving for variable 'm'.

Reorder the terms:
-11 + 2m + 8m2 = 11 + -11

Combine like terms: 11 + -11 = 0
-11 + 2m + 8m2 = 0

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

Divide each side by '8'.
-1.375 + 0.25m + m2 = 0

Move the constant term to the right:

Add '1.375' to each side of the equation.
-1.375 + 0.25m + 1.375 + m2 = 0 + 1.375

Reorder the terms:
-1.375 + 1.375 + 0.25m + m2 = 0 + 1.375

Combine like terms: -1.375 + 1.375 = 0.000
0.000 + 0.25m + m2 = 0 + 1.375
0.25m + m2 = 0 + 1.375

Combine like terms: 0 + 1.375 = 1.375
0.25m + m2 = 1.375

The m term is 0.25m.  Take half its coefficient (0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
0.25m + 0.015625 + m2 = 1.375 + 0.015625

Reorder the terms:
0.015625 + 0.25m + m2 = 1.375 + 0.015625

Combine like terms: 1.375 + 0.015625 = 1.390625
0.015625 + 0.25m + m2 = 1.390625

Factor a perfect square on the left side:
(m + 0.125)(m + 0.125) = 1.390625

Calculate the square root of the right side: 1.179247642

Break this problem into two subproblems by setting 
(m + 0.125) equal to 1.179247642 and -1.179247642.

Subproblem 1

m + 0.125 = 1.179247642 Simplifying m + 0.125 = 1.179247642 Reorder the terms: 0.125 + m = 1.179247642 Solving 0.125 + m = 1.179247642 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + m = 1.179247642 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + m = 1.179247642 + -0.125 m = 1.179247642 + -0.125 Combine like terms: 1.179247642 + -0.125 = 1.054247642 m = 1.054247642 Simplifying m = 1.054247642

Subproblem 2

m + 0.125 = -1.179247642 Simplifying m + 0.125 = -1.179247642 Reorder the terms: 0.125 + m = -1.179247642 Solving 0.125 + m = -1.179247642 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + m = -1.179247642 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + m = -1.179247642 + -0.125 m = -1.179247642 + -0.125 Combine like terms: -1.179247642 + -0.125 = -1.304247642 m = -1.304247642 Simplifying m = -1.304247642

Solution

The solution to the problem is based on the solutions from the subproblems. m = {1.054247642, -1.304247642}

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