x^2+14x=301

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Solution for x^2+14x=301 equation:


Simplifying
x2 + 14x = 301

Reorder the terms:
14x + x2 = 301

Solving
14x + x2 = 301

Solving for variable 'x'.

Reorder the terms:
-301 + 14x + x2 = 301 + -301

Combine like terms: 301 + -301 = 0
-301 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '301' to each side of the equation.
-301 + 14x + 301 + x2 = 0 + 301

Reorder the terms:
-301 + 301 + 14x + x2 = 0 + 301

Combine like terms: -301 + 301 = 0
0 + 14x + x2 = 0 + 301
14x + x2 = 0 + 301

Combine like terms: 0 + 301 = 301
14x + x2 = 301

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = 301 + 49

Reorder the terms:
49 + 14x + x2 = 301 + 49

Combine like terms: 301 + 49 = 350
49 + 14x + x2 = 350

Factor a perfect square on the left side:
(x + 7)(x + 7) = 350

Calculate the square root of the right side: 18.708286934

Break this problem into two subproblems by setting 
(x + 7) equal to 18.708286934 and -18.708286934.

Subproblem 1

x + 7 = 18.708286934 Simplifying x + 7 = 18.708286934 Reorder the terms: 7 + x = 18.708286934 Solving 7 + x = 18.708286934 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 18.708286934 + -7 Combine like terms: 7 + -7 = 0 0 + x = 18.708286934 + -7 x = 18.708286934 + -7 Combine like terms: 18.708286934 + -7 = 11.708286934 x = 11.708286934 Simplifying x = 11.708286934

Subproblem 2

x + 7 = -18.708286934 Simplifying x + 7 = -18.708286934 Reorder the terms: 7 + x = -18.708286934 Solving 7 + x = -18.708286934 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -18.708286934 + -7 Combine like terms: 7 + -7 = 0 0 + x = -18.708286934 + -7 x = -18.708286934 + -7 Combine like terms: -18.708286934 + -7 = -25.708286934 x = -25.708286934 Simplifying x = -25.708286934

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.708286934, -25.708286934}

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