7s=2s^2+4

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Solution for 7s=2s^2+4 equation:


Simplifying
7s = 2s2 + 4

Reorder the terms:
7s = 4 + 2s2

Solving
7s = 4 + 2s2

Solving for variable 's'.

Reorder the terms:
-4 + 7s + -2s2 = 4 + 2s2 + -4 + -2s2

Reorder the terms:
-4 + 7s + -2s2 = 4 + -4 + 2s2 + -2s2

Combine like terms: 4 + -4 = 0
-4 + 7s + -2s2 = 0 + 2s2 + -2s2
-4 + 7s + -2s2 = 2s2 + -2s2

Combine like terms: 2s2 + -2s2 = 0
-4 + 7s + -2s2 = 0

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

Divide each side by '-2'.
2 + -3.5s + s2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -3.5s + -2 + s2 = 0 + -2

Reorder the terms:
2 + -2 + -3.5s + s2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3.5s + s2 = 0 + -2
-3.5s + s2 = 0 + -2

Combine like terms: 0 + -2 = -2
-3.5s + s2 = -2

The s term is -3.5s.  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.
-3.5s + 3.0625 + s2 = -2 + 3.0625

Reorder the terms:
3.0625 + -3.5s + s2 = -2 + 3.0625

Combine like terms: -2 + 3.0625 = 1.0625
3.0625 + -3.5s + s2 = 1.0625

Factor a perfect square on the left side:
(s + -1.75)(s + -1.75) = 1.0625

Calculate the square root of the right side: 1.030776406

Break this problem into two subproblems by setting 
(s + -1.75) equal to 1.030776406 and -1.030776406.

Subproblem 1

s + -1.75 = 1.030776406 Simplifying s + -1.75 = 1.030776406 Reorder the terms: -1.75 + s = 1.030776406 Solving -1.75 + s = 1.030776406 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + s = 1.030776406 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + s = 1.030776406 + 1.75 s = 1.030776406 + 1.75 Combine like terms: 1.030776406 + 1.75 = 2.780776406 s = 2.780776406 Simplifying s = 2.780776406

Subproblem 2

s + -1.75 = -1.030776406 Simplifying s + -1.75 = -1.030776406 Reorder the terms: -1.75 + s = -1.030776406 Solving -1.75 + s = -1.030776406 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + s = -1.030776406 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + s = -1.030776406 + 1.75 s = -1.030776406 + 1.75 Combine like terms: -1.030776406 + 1.75 = 0.719223594 s = 0.719223594 Simplifying s = 0.719223594

Solution

The solution to the problem is based on the solutions from the subproblems. s = {2.780776406, 0.719223594}

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