x^2+6x-35=6

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Solution for x^2+6x-35=6 equation:


Simplifying
x2 + 6x + -35 = 6

Reorder the terms:
-35 + 6x + x2 = 6

Solving
-35 + 6x + x2 = 6

Solving for variable 'x'.

Reorder the terms:
-35 + -6 + 6x + x2 = 6 + -6

Combine like terms: -35 + -6 = -41
-41 + 6x + x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-41 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '41' to each side of the equation.
-41 + 6x + 41 + x2 = 0 + 41

Reorder the terms:
-41 + 41 + 6x + x2 = 0 + 41

Combine like terms: -41 + 41 = 0
0 + 6x + x2 = 0 + 41
6x + x2 = 0 + 41

Combine like terms: 0 + 41 = 41
6x + x2 = 41

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 41 + 9

Reorder the terms:
9 + 6x + x2 = 41 + 9

Combine like terms: 41 + 9 = 50
9 + 6x + x2 = 50

Factor a perfect square on the left side:
(x + 3)(x + 3) = 50

Calculate the square root of the right side: 7.071067812

Break this problem into two subproblems by setting 
(x + 3) equal to 7.071067812 and -7.071067812.

Subproblem 1

x + 3 = 7.071067812 Simplifying x + 3 = 7.071067812 Reorder the terms: 3 + x = 7.071067812 Solving 3 + x = 7.071067812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 7.071067812 + -3 Combine like terms: 3 + -3 = 0 0 + x = 7.071067812 + -3 x = 7.071067812 + -3 Combine like terms: 7.071067812 + -3 = 4.071067812 x = 4.071067812 Simplifying x = 4.071067812

Subproblem 2

x + 3 = -7.071067812 Simplifying x + 3 = -7.071067812 Reorder the terms: 3 + x = -7.071067812 Solving 3 + x = -7.071067812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -7.071067812 + -3 Combine like terms: 3 + -3 = 0 0 + x = -7.071067812 + -3 x = -7.071067812 + -3 Combine like terms: -7.071067812 + -3 = -10.071067812 x = -10.071067812 Simplifying x = -10.071067812

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.071067812, -10.071067812}

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