x^2+32x+28=0

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Solution for x^2+32x+28=0 equation:


Simplifying
x2 + 32x + 28 = 0

Reorder the terms:
28 + 32x + x2 = 0

Solving
28 + 32x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-28' to each side of the equation.
28 + 32x + -28 + x2 = 0 + -28

Reorder the terms:
28 + -28 + 32x + x2 = 0 + -28

Combine like terms: 28 + -28 = 0
0 + 32x + x2 = 0 + -28
32x + x2 = 0 + -28

Combine like terms: 0 + -28 = -28
32x + x2 = -28

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 = -28 + 256

Reorder the terms:
256 + 32x + x2 = -28 + 256

Combine like terms: -28 + 256 = 228
256 + 32x + x2 = 228

Factor a perfect square on the left side:
(x + 16)(x + 16) = 228

Calculate the square root of the right side: 15.099668871

Break this problem into two subproblems by setting 
(x + 16) equal to 15.099668871 and -15.099668871.

Subproblem 1

x + 16 = 15.099668871 Simplifying x + 16 = 15.099668871 Reorder the terms: 16 + x = 15.099668871 Solving 16 + x = 15.099668871 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 = 15.099668871 + -16 Combine like terms: 16 + -16 = 0 0 + x = 15.099668871 + -16 x = 15.099668871 + -16 Combine like terms: 15.099668871 + -16 = -0.900331129 x = -0.900331129 Simplifying x = -0.900331129

Subproblem 2

x + 16 = -15.099668871 Simplifying x + 16 = -15.099668871 Reorder the terms: 16 + x = -15.099668871 Solving 16 + x = -15.099668871 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 = -15.099668871 + -16 Combine like terms: 16 + -16 = 0 0 + x = -15.099668871 + -16 x = -15.099668871 + -16 Combine like terms: -15.099668871 + -16 = -31.099668871 x = -31.099668871 Simplifying x = -31.099668871

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.900331129, -31.099668871}

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