4x+x^2-25=2304

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Solution for 4x+x^2-25=2304 equation:


Simplifying
4x + x2 + -25 = 2304

Reorder the terms:
-25 + 4x + x2 = 2304

Solving
-25 + 4x + x2 = 2304

Solving for variable 'x'.

Reorder the terms:
-25 + -2304 + 4x + x2 = 2304 + -2304

Combine like terms: -25 + -2304 = -2329
-2329 + 4x + x2 = 2304 + -2304

Combine like terms: 2304 + -2304 = 0
-2329 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2329' to each side of the equation.
-2329 + 4x + 2329 + x2 = 0 + 2329

Reorder the terms:
-2329 + 2329 + 4x + x2 = 0 + 2329

Combine like terms: -2329 + 2329 = 0
0 + 4x + x2 = 0 + 2329
4x + x2 = 0 + 2329

Combine like terms: 0 + 2329 = 2329
4x + x2 = 2329

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 2329 + 4

Reorder the terms:
4 + 4x + x2 = 2329 + 4

Combine like terms: 2329 + 4 = 2333
4 + 4x + x2 = 2333

Factor a perfect square on the left side:
(x + 2)(x + 2) = 2333

Calculate the square root of the right side: 48.301138703

Break this problem into two subproblems by setting 
(x + 2) equal to 48.301138703 and -48.301138703.

Subproblem 1

x + 2 = 48.301138703 Simplifying x + 2 = 48.301138703 Reorder the terms: 2 + x = 48.301138703 Solving 2 + x = 48.301138703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 48.301138703 + -2 Combine like terms: 2 + -2 = 0 0 + x = 48.301138703 + -2 x = 48.301138703 + -2 Combine like terms: 48.301138703 + -2 = 46.301138703 x = 46.301138703 Simplifying x = 46.301138703

Subproblem 2

x + 2 = -48.301138703 Simplifying x + 2 = -48.301138703 Reorder the terms: 2 + x = -48.301138703 Solving 2 + x = -48.301138703 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -48.301138703 + -2 Combine like terms: 2 + -2 = 0 0 + x = -48.301138703 + -2 x = -48.301138703 + -2 Combine like terms: -48.301138703 + -2 = -50.301138703 x = -50.301138703 Simplifying x = -50.301138703

Solution

The solution to the problem is based on the solutions from the subproblems. x = {46.301138703, -50.301138703}

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