m^2+10m-7=

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


Simplifying
m2 + 10m + -7 = 0

Reorder the terms:
-7 + 10m + m2 = 0

Solving
-7 + 10m + m2 = 0

Solving for variable 'm'.

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 10m + 7 + m2 = 0 + 7

Reorder the terms:
-7 + 7 + 10m + m2 = 0 + 7

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

Combine like terms: 0 + 7 = 7
10m + m2 = 7

The m term is 10m.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10m + 25 + m2 = 7 + 25

Reorder the terms:
25 + 10m + m2 = 7 + 25

Combine like terms: 7 + 25 = 32
25 + 10m + m2 = 32

Factor a perfect square on the left side:
(m + 5)(m + 5) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(m + 5) equal to 5.656854249 and -5.656854249.

Subproblem 1

m + 5 = 5.656854249 Simplifying m + 5 = 5.656854249 Reorder the terms: 5 + m = 5.656854249 Solving 5 + m = 5.656854249 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + m = 5.656854249 + -5 Combine like terms: 5 + -5 = 0 0 + m = 5.656854249 + -5 m = 5.656854249 + -5 Combine like terms: 5.656854249 + -5 = 0.656854249 m = 0.656854249 Simplifying m = 0.656854249

Subproblem 2

m + 5 = -5.656854249 Simplifying m + 5 = -5.656854249 Reorder the terms: 5 + m = -5.656854249 Solving 5 + m = -5.656854249 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + m = -5.656854249 + -5 Combine like terms: 5 + -5 = 0 0 + m = -5.656854249 + -5 m = -5.656854249 + -5 Combine like terms: -5.656854249 + -5 = -10.656854249 m = -10.656854249 Simplifying m = -10.656854249

Solution

The solution to the problem is based on the solutions from the subproblems. m = {0.656854249, -10.656854249}

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