x^2-16x-2=-30x

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Solution for x^2-16x-2=-30x equation:


Simplifying
x2 + -16x + -2 = -30x

Reorder the terms:
-2 + -16x + x2 = -30x

Solving
-2 + -16x + x2 = -30x

Solving for variable 'x'.

Reorder the terms:
-2 + -16x + 30x + x2 = -30x + 30x

Combine like terms: -16x + 30x = 14x
-2 + 14x + x2 = -30x + 30x

Combine like terms: -30x + 30x = 0
-2 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 14x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 14x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 14x + x2 = 0 + 2
14x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
14x + x2 = 2

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 = 2 + 49

Reorder the terms:
49 + 14x + x2 = 2 + 49

Combine like terms: 2 + 49 = 51
49 + 14x + x2 = 51

Factor a perfect square on the left side:
(x + 7)(x + 7) = 51

Calculate the square root of the right side: 7.141428429

Break this problem into two subproblems by setting 
(x + 7) equal to 7.141428429 and -7.141428429.

Subproblem 1

x + 7 = 7.141428429 Simplifying x + 7 = 7.141428429 Reorder the terms: 7 + x = 7.141428429 Solving 7 + x = 7.141428429 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 = 7.141428429 + -7 Combine like terms: 7 + -7 = 0 0 + x = 7.141428429 + -7 x = 7.141428429 + -7 Combine like terms: 7.141428429 + -7 = 0.141428429 x = 0.141428429 Simplifying x = 0.141428429

Subproblem 2

x + 7 = -7.141428429 Simplifying x + 7 = -7.141428429 Reorder the terms: 7 + x = -7.141428429 Solving 7 + x = -7.141428429 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 = -7.141428429 + -7 Combine like terms: 7 + -7 = 0 0 + x = -7.141428429 + -7 x = -7.141428429 + -7 Combine like terms: -7.141428429 + -7 = -14.141428429 x = -14.141428429 Simplifying x = -14.141428429

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.141428429, -14.141428429}

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