2x+16=x^2+32x

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Solution for 2x+16=x^2+32x equation:


Simplifying
2x + 16 = x2 + 32x

Reorder the terms:
16 + 2x = x2 + 32x

Reorder the terms:
16 + 2x = 32x + x2

Solving
16 + 2x = 32x + x2

Solving for variable 'x'.

Combine like terms: 2x + -32x = -30x
16 + -30x + -1x2 = 32x + x2 + -32x + -1x2

Reorder the terms:
16 + -30x + -1x2 = 32x + -32x + x2 + -1x2

Combine like terms: 32x + -32x = 0
16 + -30x + -1x2 = 0 + x2 + -1x2
16 + -30x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
16 + -30x + -1x2 = 0

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

Divide each side by '-1'.
-16 + 30x + x2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 30x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + 30x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 30x + x2 = 0 + 16
30x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
30x + x2 = 16

The x term is 30x.  Take half its coefficient (15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
30x + 225 + x2 = 16 + 225

Reorder the terms:
225 + 30x + x2 = 16 + 225

Combine like terms: 16 + 225 = 241
225 + 30x + x2 = 241

Factor a perfect square on the left side:
(x + 15)(x + 15) = 241

Calculate the square root of the right side: 15.524174696

Break this problem into two subproblems by setting 
(x + 15) equal to 15.524174696 and -15.524174696.

Subproblem 1

x + 15 = 15.524174696 Simplifying x + 15 = 15.524174696 Reorder the terms: 15 + x = 15.524174696 Solving 15 + x = 15.524174696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 15.524174696 + -15 Combine like terms: 15 + -15 = 0 0 + x = 15.524174696 + -15 x = 15.524174696 + -15 Combine like terms: 15.524174696 + -15 = 0.524174696 x = 0.524174696 Simplifying x = 0.524174696

Subproblem 2

x + 15 = -15.524174696 Simplifying x + 15 = -15.524174696 Reorder the terms: 15 + x = -15.524174696 Solving 15 + x = -15.524174696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -15.524174696 + -15 Combine like terms: 15 + -15 = 0 0 + x = -15.524174696 + -15 x = -15.524174696 + -15 Combine like terms: -15.524174696 + -15 = -30.524174696 x = -30.524174696 Simplifying x = -30.524174696

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.524174696, -30.524174696}

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