x^2-6=-7x

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Solution for x^2-6=-7x equation:


Simplifying
x2 + -6 = -7x

Reorder the terms:
-6 + x2 = -7x

Solving
-6 + x2 = -7x

Solving for variable 'x'.

Reorder the terms:
-6 + 7x + x2 = -7x + 7x

Combine like terms: -7x + 7x = 0
-6 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 7x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + 7x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 7x + x2 = 0 + 6
7x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
7x + x2 = 6

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 6 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 6 + 12.25

Combine like terms: 6 + 12.25 = 18.25
12.25 + 7x + x2 = 18.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(x + 3.5) equal to 4.272001873 and -4.272001873.

Subproblem 1

x + 3.5 = 4.272001873 Simplifying x + 3.5 = 4.272001873 Reorder the terms: 3.5 + x = 4.272001873 Solving 3.5 + x = 4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 4.272001873 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 4.272001873 + -3.5 x = 4.272001873 + -3.5 Combine like terms: 4.272001873 + -3.5 = 0.772001873 x = 0.772001873 Simplifying x = 0.772001873

Subproblem 2

x + 3.5 = -4.272001873 Simplifying x + 3.5 = -4.272001873 Reorder the terms: 3.5 + x = -4.272001873 Solving 3.5 + x = -4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -4.272001873 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -4.272001873 + -3.5 x = -4.272001873 + -3.5 Combine like terms: -4.272001873 + -3.5 = -7.772001873 x = -7.772001873 Simplifying x = -7.772001873

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.772001873, -7.772001873}

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