8m^2-7m+1=0

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Solution for 8m^2-7m+1=0 equation:


Simplifying
8m2 + -7m + 1 = 0

Reorder the terms:
1 + -7m + 8m2 = 0

Solving
1 + -7m + 8m2 = 0

Solving for variable 'm'.

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

Divide each side by '8'.
0.125 + -0.875m + m2 = 0

Move the constant term to the right:

Add '-0.125' to each side of the equation.
0.125 + -0.875m + -0.125 + m2 = 0 + -0.125

Reorder the terms:
0.125 + -0.125 + -0.875m + m2 = 0 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + -0.875m + m2 = 0 + -0.125
-0.875m + m2 = 0 + -0.125

Combine like terms: 0 + -0.125 = -0.125
-0.875m + m2 = -0.125

The m term is -0.875m.  Take half its coefficient (-0.4375).
Square it (0.19140625) and add it to both sides.

Add '0.19140625' to each side of the equation.
-0.875m + 0.19140625 + m2 = -0.125 + 0.19140625

Reorder the terms:
0.19140625 + -0.875m + m2 = -0.125 + 0.19140625

Combine like terms: -0.125 + 0.19140625 = 0.06640625
0.19140625 + -0.875m + m2 = 0.06640625

Factor a perfect square on the left side:
(m + -0.4375)(m + -0.4375) = 0.06640625

Calculate the square root of the right side: 0.257694102

Break this problem into two subproblems by setting 
(m + -0.4375) equal to 0.257694102 and -0.257694102.

Subproblem 1

m + -0.4375 = 0.257694102 Simplifying m + -0.4375 = 0.257694102 Reorder the terms: -0.4375 + m = 0.257694102 Solving -0.4375 + m = 0.257694102 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + m = 0.257694102 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + m = 0.257694102 + 0.4375 m = 0.257694102 + 0.4375 Combine like terms: 0.257694102 + 0.4375 = 0.695194102 m = 0.695194102 Simplifying m = 0.695194102

Subproblem 2

m + -0.4375 = -0.257694102 Simplifying m + -0.4375 = -0.257694102 Reorder the terms: -0.4375 + m = -0.257694102 Solving -0.4375 + m = -0.257694102 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + m = -0.257694102 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + m = -0.257694102 + 0.4375 m = -0.257694102 + 0.4375 Combine like terms: -0.257694102 + 0.4375 = 0.179805898 m = 0.179805898 Simplifying m = 0.179805898

Solution

The solution to the problem is based on the solutions from the subproblems. m = {0.695194102, 0.179805898}

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