70=0.1m^2+5m

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Solution for 70=0.1m^2+5m equation:


Simplifying
70 = 0.1m2 + 5m

Reorder the terms:
70 = 5m + 0.1m2

Solving
70 = 5m + 0.1m2

Solving for variable 'm'.

Reorder the terms:
70 + -5m + -0.1m2 = 5m + -5m + 0.1m2 + -0.1m2

Combine like terms: 5m + -5m = 0
70 + -5m + -0.1m2 = 0 + 0.1m2 + -0.1m2
70 + -5m + -0.1m2 = 0.1m2 + -0.1m2

Combine like terms: 0.1m2 + -0.1m2 = 0.0
70 + -5m + -0.1m2 = 0.0

Begin completing the square.  Divide all terms by
-0.1 the coefficient of the squared term: 

Divide each side by '-0.1'.
-700 + 50m + m2 = 0

Move the constant term to the right:

Add '700' to each side of the equation.
-700 + 50m + 700 + m2 = 0 + 700

Reorder the terms:
-700 + 700 + 50m + m2 = 0 + 700

Combine like terms: -700 + 700 = 0
0 + 50m + m2 = 0 + 700
50m + m2 = 0 + 700

Combine like terms: 0 + 700 = 700
50m + m2 = 700

The m term is 50m.  Take half its coefficient (25).
Square it (625) and add it to both sides.

Add '625' to each side of the equation.
50m + 625 + m2 = 700 + 625

Reorder the terms:
625 + 50m + m2 = 700 + 625

Combine like terms: 700 + 625 = 1325
625 + 50m + m2 = 1325

Factor a perfect square on the left side:
(m + 25)(m + 25) = 1325

Calculate the square root of the right side: 36.400549446

Break this problem into two subproblems by setting 
(m + 25) equal to 36.400549446 and -36.400549446.

Subproblem 1

m + 25 = 36.400549446 Simplifying m + 25 = 36.400549446 Reorder the terms: 25 + m = 36.400549446 Solving 25 + m = 36.400549446 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + m = 36.400549446 + -25 Combine like terms: 25 + -25 = 0 0 + m = 36.400549446 + -25 m = 36.400549446 + -25 Combine like terms: 36.400549446 + -25 = 11.400549446 m = 11.400549446 Simplifying m = 11.400549446

Subproblem 2

m + 25 = -36.400549446 Simplifying m + 25 = -36.400549446 Reorder the terms: 25 + m = -36.400549446 Solving 25 + m = -36.400549446 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + m = -36.400549446 + -25 Combine like terms: 25 + -25 = 0 0 + m = -36.400549446 + -25 m = -36.400549446 + -25 Combine like terms: -36.400549446 + -25 = -61.400549446 m = -61.400549446 Simplifying m = -61.400549446

Solution

The solution to the problem is based on the solutions from the subproblems. m = {11.400549446, -61.400549446}

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