25s^2+20s=4

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Solution for 25s^2+20s=4 equation:


Simplifying
25s2 + 20s = 4

Reorder the terms:
20s + 25s2 = 4

Solving
20s + 25s2 = 4

Solving for variable 's'.

Reorder the terms:
-4 + 20s + 25s2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + 20s + 25s2 = 0

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

Divide each side by '25'.
-0.16 + 0.8s + s2 = 0

Move the constant term to the right:

Add '0.16' to each side of the equation.
-0.16 + 0.8s + 0.16 + s2 = 0 + 0.16

Reorder the terms:
-0.16 + 0.16 + 0.8s + s2 = 0 + 0.16

Combine like terms: -0.16 + 0.16 = 0.00
0.00 + 0.8s + s2 = 0 + 0.16
0.8s + s2 = 0 + 0.16

Combine like terms: 0 + 0.16 = 0.16
0.8s + s2 = 0.16

The s term is 0.8s.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8s + 0.16 + s2 = 0.16 + 0.16

Reorder the terms:
0.16 + 0.8s + s2 = 0.16 + 0.16

Combine like terms: 0.16 + 0.16 = 0.32
0.16 + 0.8s + s2 = 0.32

Factor a perfect square on the left side:
(s + 0.4)(s + 0.4) = 0.32

Calculate the square root of the right side: 0.565685425

Break this problem into two subproblems by setting 
(s + 0.4) equal to 0.565685425 and -0.565685425.

Subproblem 1

s + 0.4 = 0.565685425 Simplifying s + 0.4 = 0.565685425 Reorder the terms: 0.4 + s = 0.565685425 Solving 0.4 + s = 0.565685425 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + s = 0.565685425 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + s = 0.565685425 + -0.4 s = 0.565685425 + -0.4 Combine like terms: 0.565685425 + -0.4 = 0.165685425 s = 0.165685425 Simplifying s = 0.165685425

Subproblem 2

s + 0.4 = -0.565685425 Simplifying s + 0.4 = -0.565685425 Reorder the terms: 0.4 + s = -0.565685425 Solving 0.4 + s = -0.565685425 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + s = -0.565685425 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + s = -0.565685425 + -0.4 s = -0.565685425 + -0.4 Combine like terms: -0.565685425 + -0.4 = -0.965685425 s = -0.965685425 Simplifying s = -0.965685425

Solution

The solution to the problem is based on the solutions from the subproblems. s = {0.165685425, -0.965685425}

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