48x+x^2=540

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Solution for 48x+x^2=540 equation:


Simplifying
48x + x2 = 540

Solving
48x + x2 = 540

Solving for variable 'x'.

Reorder the terms:
-540 + 48x + x2 = 540 + -540

Combine like terms: 540 + -540 = 0
-540 + 48x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '540' to each side of the equation.
-540 + 48x + 540 + x2 = 0 + 540

Reorder the terms:
-540 + 540 + 48x + x2 = 0 + 540

Combine like terms: -540 + 540 = 0
0 + 48x + x2 = 0 + 540
48x + x2 = 0 + 540

Combine like terms: 0 + 540 = 540
48x + x2 = 540

The x term is 48x.  Take half its coefficient (24).
Square it (576) and add it to both sides.

Add '576' to each side of the equation.
48x + 576 + x2 = 540 + 576

Reorder the terms:
576 + 48x + x2 = 540 + 576

Combine like terms: 540 + 576 = 1116
576 + 48x + x2 = 1116

Factor a perfect square on the left side:
(x + 24)(x + 24) = 1116

Calculate the square root of the right side: 33.406586177

Break this problem into two subproblems by setting 
(x + 24) equal to 33.406586177 and -33.406586177.

Subproblem 1

x + 24 = 33.406586177 Simplifying x + 24 = 33.406586177 Reorder the terms: 24 + x = 33.406586177 Solving 24 + x = 33.406586177 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + x = 33.406586177 + -24 Combine like terms: 24 + -24 = 0 0 + x = 33.406586177 + -24 x = 33.406586177 + -24 Combine like terms: 33.406586177 + -24 = 9.406586177 x = 9.406586177 Simplifying x = 9.406586177

Subproblem 2

x + 24 = -33.406586177 Simplifying x + 24 = -33.406586177 Reorder the terms: 24 + x = -33.406586177 Solving 24 + x = -33.406586177 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + x = -33.406586177 + -24 Combine like terms: 24 + -24 = 0 0 + x = -33.406586177 + -24 x = -33.406586177 + -24 Combine like terms: -33.406586177 + -24 = -57.406586177 x = -57.406586177 Simplifying x = -57.406586177

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.406586177, -57.406586177}

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