2m^2-7m-23=10

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Solution for 2m^2-7m-23=10 equation:


Simplifying
2m2 + -7m + -23 = 10

Reorder the terms:
-23 + -7m + 2m2 = 10

Solving
-23 + -7m + 2m2 = 10

Solving for variable 'm'.

Reorder the terms:
-23 + -10 + -7m + 2m2 = 10 + -10

Combine like terms: -23 + -10 = -33
-33 + -7m + 2m2 = 10 + -10

Combine like terms: 10 + -10 = 0
-33 + -7m + 2m2 = 0

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

Divide each side by '2'.
-16.5 + -3.5m + m2 = 0

Move the constant term to the right:

Add '16.5' to each side of the equation.
-16.5 + -3.5m + 16.5 + m2 = 0 + 16.5

Reorder the terms:
-16.5 + 16.5 + -3.5m + m2 = 0 + 16.5

Combine like terms: -16.5 + 16.5 = 0.0
0.0 + -3.5m + m2 = 0 + 16.5
-3.5m + m2 = 0 + 16.5

Combine like terms: 0 + 16.5 = 16.5
-3.5m + m2 = 16.5

The m term is -3.5m.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5m + 3.0625 + m2 = 16.5 + 3.0625

Reorder the terms:
3.0625 + -3.5m + m2 = 16.5 + 3.0625

Combine like terms: 16.5 + 3.0625 = 19.5625
3.0625 + -3.5m + m2 = 19.5625

Factor a perfect square on the left side:
(m + -1.75)(m + -1.75) = 19.5625

Calculate the square root of the right side: 4.422951503

Break this problem into two subproblems by setting 
(m + -1.75) equal to 4.422951503 and -4.422951503.

Subproblem 1

m + -1.75 = 4.422951503 Simplifying m + -1.75 = 4.422951503 Reorder the terms: -1.75 + m = 4.422951503 Solving -1.75 + m = 4.422951503 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + m = 4.422951503 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + m = 4.422951503 + 1.75 m = 4.422951503 + 1.75 Combine like terms: 4.422951503 + 1.75 = 6.172951503 m = 6.172951503 Simplifying m = 6.172951503

Subproblem 2

m + -1.75 = -4.422951503 Simplifying m + -1.75 = -4.422951503 Reorder the terms: -1.75 + m = -4.422951503 Solving -1.75 + m = -4.422951503 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + m = -4.422951503 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + m = -4.422951503 + 1.75 m = -4.422951503 + 1.75 Combine like terms: -4.422951503 + 1.75 = -2.672951503 m = -2.672951503 Simplifying m = -2.672951503

Solution

The solution to the problem is based on the solutions from the subproblems. m = {6.172951503, -2.672951503}

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