4m^2+7m=25

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Solution for 4m^2+7m=25 equation:


Simplifying
4m2 + 7m = 25

Reorder the terms:
7m + 4m2 = 25

Solving
7m + 4m2 = 25

Solving for variable 'm'.

Reorder the terms:
-25 + 7m + 4m2 = 25 + -25

Combine like terms: 25 + -25 = 0
-25 + 7m + 4m2 = 0

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

Divide each side by '4'.
-6.25 + 1.75m + m2 = 0

Move the constant term to the right:

Add '6.25' to each side of the equation.
-6.25 + 1.75m + 6.25 + m2 = 0 + 6.25

Reorder the terms:
-6.25 + 6.25 + 1.75m + m2 = 0 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + 1.75m + m2 = 0 + 6.25
1.75m + m2 = 0 + 6.25

Combine like terms: 0 + 6.25 = 6.25
1.75m + m2 = 6.25

The m term is 1.75m.  Take half its coefficient (0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
1.75m + 0.765625 + m2 = 6.25 + 0.765625

Reorder the terms:
0.765625 + 1.75m + m2 = 6.25 + 0.765625

Combine like terms: 6.25 + 0.765625 = 7.015625
0.765625 + 1.75m + m2 = 7.015625

Factor a perfect square on the left side:
(m + 0.875)(m + 0.875) = 7.015625

Calculate the square root of the right side: 2.648702513

Break this problem into two subproblems by setting 
(m + 0.875) equal to 2.648702513 and -2.648702513.

Subproblem 1

m + 0.875 = 2.648702513 Simplifying m + 0.875 = 2.648702513 Reorder the terms: 0.875 + m = 2.648702513 Solving 0.875 + m = 2.648702513 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + m = 2.648702513 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + m = 2.648702513 + -0.875 m = 2.648702513 + -0.875 Combine like terms: 2.648702513 + -0.875 = 1.773702513 m = 1.773702513 Simplifying m = 1.773702513

Subproblem 2

m + 0.875 = -2.648702513 Simplifying m + 0.875 = -2.648702513 Reorder the terms: 0.875 + m = -2.648702513 Solving 0.875 + m = -2.648702513 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + m = -2.648702513 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + m = -2.648702513 + -0.875 m = -2.648702513 + -0.875 Combine like terms: -2.648702513 + -0.875 = -3.523702513 m = -3.523702513 Simplifying m = -3.523702513

Solution

The solution to the problem is based on the solutions from the subproblems. m = {1.773702513, -3.523702513}

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