x^2+8x=14

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Solution for x^2+8x=14 equation:


Simplifying
x2 + 8x = 14

Reorder the terms:
8x + x2 = 14

Solving
8x + x2 = 14

Solving for variable 'x'.

Reorder the terms:
-14 + 8x + x2 = 14 + -14

Combine like terms: 14 + -14 = 0
-14 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + 8x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + 8x + x2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + 8x + x2 = 0 + 14
8x + x2 = 0 + 14

Combine like terms: 0 + 14 = 14
8x + x2 = 14

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 14 + 16

Reorder the terms:
16 + 8x + x2 = 14 + 16

Combine like terms: 14 + 16 = 30
16 + 8x + x2 = 30

Factor a perfect square on the left side:
(x + 4)(x + 4) = 30

Calculate the square root of the right side: 5.477225575

Break this problem into two subproblems by setting 
(x + 4) equal to 5.477225575 and -5.477225575.

Subproblem 1

x + 4 = 5.477225575 Simplifying x + 4 = 5.477225575 Reorder the terms: 4 + x = 5.477225575 Solving 4 + x = 5.477225575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 5.477225575 + -4 Combine like terms: 4 + -4 = 0 0 + x = 5.477225575 + -4 x = 5.477225575 + -4 Combine like terms: 5.477225575 + -4 = 1.477225575 x = 1.477225575 Simplifying x = 1.477225575

Subproblem 2

x + 4 = -5.477225575 Simplifying x + 4 = -5.477225575 Reorder the terms: 4 + x = -5.477225575 Solving 4 + x = -5.477225575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -5.477225575 + -4 Combine like terms: 4 + -4 = 0 0 + x = -5.477225575 + -4 x = -5.477225575 + -4 Combine like terms: -5.477225575 + -4 = -9.477225575 x = -9.477225575 Simplifying x = -9.477225575

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.477225575, -9.477225575}

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