x^2+32x=54

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Solution for x^2+32x=54 equation:


Simplifying
x2 + 32x = 54

Reorder the terms:
32x + x2 = 54

Solving
32x + x2 = 54

Solving for variable 'x'.

Reorder the terms:
-54 + 32x + x2 = 54 + -54

Combine like terms: 54 + -54 = 0
-54 + 32x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '54' to each side of the equation.
-54 + 32x + 54 + x2 = 0 + 54

Reorder the terms:
-54 + 54 + 32x + x2 = 0 + 54

Combine like terms: -54 + 54 = 0
0 + 32x + x2 = 0 + 54
32x + x2 = 0 + 54

Combine like terms: 0 + 54 = 54
32x + x2 = 54

The x term is 32x.  Take half its coefficient (16).
Square it (256) and add it to both sides.

Add '256' to each side of the equation.
32x + 256 + x2 = 54 + 256

Reorder the terms:
256 + 32x + x2 = 54 + 256

Combine like terms: 54 + 256 = 310
256 + 32x + x2 = 310

Factor a perfect square on the left side:
(x + 16)(x + 16) = 310

Calculate the square root of the right side: 17.606816862

Break this problem into two subproblems by setting 
(x + 16) equal to 17.606816862 and -17.606816862.

Subproblem 1

x + 16 = 17.606816862 Simplifying x + 16 = 17.606816862 Reorder the terms: 16 + x = 17.606816862 Solving 16 + x = 17.606816862 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = 17.606816862 + -16 Combine like terms: 16 + -16 = 0 0 + x = 17.606816862 + -16 x = 17.606816862 + -16 Combine like terms: 17.606816862 + -16 = 1.606816862 x = 1.606816862 Simplifying x = 1.606816862

Subproblem 2

x + 16 = -17.606816862 Simplifying x + 16 = -17.606816862 Reorder the terms: 16 + x = -17.606816862 Solving 16 + x = -17.606816862 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = -17.606816862 + -16 Combine like terms: 16 + -16 = 0 0 + x = -17.606816862 + -16 x = -17.606816862 + -16 Combine like terms: -17.606816862 + -16 = -33.606816862 x = -33.606816862 Simplifying x = -33.606816862

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.606816862, -33.606816862}

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