x^2+28x-1176=0

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Solution for x^2+28x-1176=0 equation:


Simplifying
x2 + 28x + -1176 = 0

Reorder the terms:
-1176 + 28x + x2 = 0

Solving
-1176 + 28x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1176' to each side of the equation.
-1176 + 28x + 1176 + x2 = 0 + 1176

Reorder the terms:
-1176 + 1176 + 28x + x2 = 0 + 1176

Combine like terms: -1176 + 1176 = 0
0 + 28x + x2 = 0 + 1176
28x + x2 = 0 + 1176

Combine like terms: 0 + 1176 = 1176
28x + x2 = 1176

The x term is 28x.  Take half its coefficient (14).
Square it (196) and add it to both sides.

Add '196' to each side of the equation.
28x + 196 + x2 = 1176 + 196

Reorder the terms:
196 + 28x + x2 = 1176 + 196

Combine like terms: 1176 + 196 = 1372
196 + 28x + x2 = 1372

Factor a perfect square on the left side:
(x + 14)(x + 14) = 1372

Calculate the square root of the right side: 37.040518355

Break this problem into two subproblems by setting 
(x + 14) equal to 37.040518355 and -37.040518355.

Subproblem 1

x + 14 = 37.040518355 Simplifying x + 14 = 37.040518355 Reorder the terms: 14 + x = 37.040518355 Solving 14 + x = 37.040518355 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 37.040518355 + -14 Combine like terms: 14 + -14 = 0 0 + x = 37.040518355 + -14 x = 37.040518355 + -14 Combine like terms: 37.040518355 + -14 = 23.040518355 x = 23.040518355 Simplifying x = 23.040518355

Subproblem 2

x + 14 = -37.040518355 Simplifying x + 14 = -37.040518355 Reorder the terms: 14 + x = -37.040518355 Solving 14 + x = -37.040518355 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = -37.040518355 + -14 Combine like terms: 14 + -14 = 0 0 + x = -37.040518355 + -14 x = -37.040518355 + -14 Combine like terms: -37.040518355 + -14 = -51.040518355 x = -51.040518355 Simplifying x = -51.040518355

Solution

The solution to the problem is based on the solutions from the subproblems. x = {23.040518355, -51.040518355}

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