2m^2+m-5=2m+7

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Solution for 2m^2+m-5=2m+7 equation:


Simplifying
2m2 + m + -5 = 2m + 7

Reorder the terms:
-5 + m + 2m2 = 2m + 7

Reorder the terms:
-5 + m + 2m2 = 7 + 2m

Solving
-5 + m + 2m2 = 7 + 2m

Solving for variable 'm'.

Reorder the terms:
-5 + -7 + m + -2m + 2m2 = 7 + 2m + -7 + -2m

Combine like terms: -5 + -7 = -12
-12 + m + -2m + 2m2 = 7 + 2m + -7 + -2m

Combine like terms: m + -2m = -1m
-12 + -1m + 2m2 = 7 + 2m + -7 + -2m

Reorder the terms:
-12 + -1m + 2m2 = 7 + -7 + 2m + -2m

Combine like terms: 7 + -7 = 0
-12 + -1m + 2m2 = 0 + 2m + -2m
-12 + -1m + 2m2 = 2m + -2m

Combine like terms: 2m + -2m = 0
-12 + -1m + 2m2 = 0

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

Divide each side by '2'.
-6 + -0.5m + m2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -0.5m + 6 + m2 = 0 + 6

Reorder the terms:
-6 + 6 + -0.5m + m2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -0.5m + m2 = 0 + 6
-0.5m + m2 = 0 + 6

Combine like terms: 0 + 6 = 6
-0.5m + m2 = 6

The m term is -0.5m.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5m + 0.0625 + m2 = 6 + 0.0625

Reorder the terms:
0.0625 + -0.5m + m2 = 6 + 0.0625

Combine like terms: 6 + 0.0625 = 6.0625
0.0625 + -0.5m + m2 = 6.0625

Factor a perfect square on the left side:
(m + -0.25)(m + -0.25) = 6.0625

Calculate the square root of the right side: 2.46221445

Break this problem into two subproblems by setting 
(m + -0.25) equal to 2.46221445 and -2.46221445.

Subproblem 1

m + -0.25 = 2.46221445 Simplifying m + -0.25 = 2.46221445 Reorder the terms: -0.25 + m = 2.46221445 Solving -0.25 + m = 2.46221445 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + m = 2.46221445 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + m = 2.46221445 + 0.25 m = 2.46221445 + 0.25 Combine like terms: 2.46221445 + 0.25 = 2.71221445 m = 2.71221445 Simplifying m = 2.71221445

Subproblem 2

m + -0.25 = -2.46221445 Simplifying m + -0.25 = -2.46221445 Reorder the terms: -0.25 + m = -2.46221445 Solving -0.25 + m = -2.46221445 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + m = -2.46221445 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + m = -2.46221445 + 0.25 m = -2.46221445 + 0.25 Combine like terms: -2.46221445 + 0.25 = -2.21221445 m = -2.21221445 Simplifying m = -2.21221445

Solution

The solution to the problem is based on the solutions from the subproblems. m = {2.71221445, -2.21221445}

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