x^2+4x-92=9

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Solution for x^2+4x-92=9 equation:


Simplifying
x2 + 4x + -92 = 9

Reorder the terms:
-92 + 4x + x2 = 9

Solving
-92 + 4x + x2 = 9

Solving for variable 'x'.

Reorder the terms:
-92 + -9 + 4x + x2 = 9 + -9

Combine like terms: -92 + -9 = -101
-101 + 4x + x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-101 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '101' to each side of the equation.
-101 + 4x + 101 + x2 = 0 + 101

Reorder the terms:
-101 + 101 + 4x + x2 = 0 + 101

Combine like terms: -101 + 101 = 0
0 + 4x + x2 = 0 + 101
4x + x2 = 0 + 101

Combine like terms: 0 + 101 = 101
4x + x2 = 101

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 101 + 4

Reorder the terms:
4 + 4x + x2 = 101 + 4

Combine like terms: 101 + 4 = 105
4 + 4x + x2 = 105

Factor a perfect square on the left side:
(x + 2)(x + 2) = 105

Calculate the square root of the right side: 10.246950766

Break this problem into two subproblems by setting 
(x + 2) equal to 10.246950766 and -10.246950766.

Subproblem 1

x + 2 = 10.246950766 Simplifying x + 2 = 10.246950766 Reorder the terms: 2 + x = 10.246950766 Solving 2 + x = 10.246950766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 10.246950766 + -2 Combine like terms: 2 + -2 = 0 0 + x = 10.246950766 + -2 x = 10.246950766 + -2 Combine like terms: 10.246950766 + -2 = 8.246950766 x = 8.246950766 Simplifying x = 8.246950766

Subproblem 2

x + 2 = -10.246950766 Simplifying x + 2 = -10.246950766 Reorder the terms: 2 + x = -10.246950766 Solving 2 + x = -10.246950766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -10.246950766 + -2 Combine like terms: 2 + -2 = 0 0 + x = -10.246950766 + -2 x = -10.246950766 + -2 Combine like terms: -10.246950766 + -2 = -12.246950766 x = -12.246950766 Simplifying x = -12.246950766

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.246950766, -12.246950766}

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