x^2+28x-1239=0

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Solution for x^2+28x-1239=0 equation:


Simplifying
x2 + 28x + -1239 = 0

Reorder the terms:
-1239 + 28x + x2 = 0

Solving
-1239 + 28x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1239' to each side of the equation.
-1239 + 28x + 1239 + x2 = 0 + 1239

Reorder the terms:
-1239 + 1239 + 28x + x2 = 0 + 1239

Combine like terms: -1239 + 1239 = 0
0 + 28x + x2 = 0 + 1239
28x + x2 = 0 + 1239

Combine like terms: 0 + 1239 = 1239
28x + x2 = 1239

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 = 1239 + 196

Reorder the terms:
196 + 28x + x2 = 1239 + 196

Combine like terms: 1239 + 196 = 1435
196 + 28x + x2 = 1435

Factor a perfect square on the left side:
(x + 14)(x + 14) = 1435

Calculate the square root of the right side: 37.88139385

Break this problem into two subproblems by setting 
(x + 14) equal to 37.88139385 and -37.88139385.

Subproblem 1

x + 14 = 37.88139385 Simplifying x + 14 = 37.88139385 Reorder the terms: 14 + x = 37.88139385 Solving 14 + x = 37.88139385 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 = 37.88139385 + -14 Combine like terms: 14 + -14 = 0 0 + x = 37.88139385 + -14 x = 37.88139385 + -14 Combine like terms: 37.88139385 + -14 = 23.88139385 x = 23.88139385 Simplifying x = 23.88139385

Subproblem 2

x + 14 = -37.88139385 Simplifying x + 14 = -37.88139385 Reorder the terms: 14 + x = -37.88139385 Solving 14 + x = -37.88139385 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 = -37.88139385 + -14 Combine like terms: 14 + -14 = 0 0 + x = -37.88139385 + -14 x = -37.88139385 + -14 Combine like terms: -37.88139385 + -14 = -51.88139385 x = -51.88139385 Simplifying x = -51.88139385

Solution

The solution to the problem is based on the solutions from the subproblems. x = {23.88139385, -51.88139385}

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