4x+25=x^2+100x

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Solution for 4x+25=x^2+100x equation:


Simplifying
4x + 25 = x2 + 100x

Reorder the terms:
25 + 4x = x2 + 100x

Reorder the terms:
25 + 4x = 100x + x2

Solving
25 + 4x = 100x + x2

Solving for variable 'x'.

Combine like terms: 4x + -100x = -96x
25 + -96x + -1x2 = 100x + x2 + -100x + -1x2

Reorder the terms:
25 + -96x + -1x2 = 100x + -100x + x2 + -1x2

Combine like terms: 100x + -100x = 0
25 + -96x + -1x2 = 0 + x2 + -1x2
25 + -96x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
25 + -96x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-25 + 96x + x2 = 0

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + 96x + 25 + x2 = 0 + 25

Reorder the terms:
-25 + 25 + 96x + x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 96x + x2 = 0 + 25
96x + x2 = 0 + 25

Combine like terms: 0 + 25 = 25
96x + x2 = 25

The x term is 96x.  Take half its coefficient (48).
Square it (2304) and add it to both sides.

Add '2304' to each side of the equation.
96x + 2304 + x2 = 25 + 2304

Reorder the terms:
2304 + 96x + x2 = 25 + 2304

Combine like terms: 25 + 2304 = 2329
2304 + 96x + x2 = 2329

Factor a perfect square on the left side:
(x + 48)(x + 48) = 2329

Calculate the square root of the right side: 48.259714048

Break this problem into two subproblems by setting 
(x + 48) equal to 48.259714048 and -48.259714048.

Subproblem 1

x + 48 = 48.259714048 Simplifying x + 48 = 48.259714048 Reorder the terms: 48 + x = 48.259714048 Solving 48 + x = 48.259714048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-48' to each side of the equation. 48 + -48 + x = 48.259714048 + -48 Combine like terms: 48 + -48 = 0 0 + x = 48.259714048 + -48 x = 48.259714048 + -48 Combine like terms: 48.259714048 + -48 = 0.259714048 x = 0.259714048 Simplifying x = 0.259714048

Subproblem 2

x + 48 = -48.259714048 Simplifying x + 48 = -48.259714048 Reorder the terms: 48 + x = -48.259714048 Solving 48 + x = -48.259714048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-48' to each side of the equation. 48 + -48 + x = -48.259714048 + -48 Combine like terms: 48 + -48 = 0 0 + x = -48.259714048 + -48 x = -48.259714048 + -48 Combine like terms: -48.259714048 + -48 = -96.259714048 x = -96.259714048 Simplifying x = -96.259714048

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.259714048, -96.259714048}

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