7x+x^2=-2

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


Simplifying
7x + x2 = -2

Solving
7x + x2 = -2

Solving for variable 'x'.

Reorder the terms:
2 + 7x + x2 = -2 + 2

Combine like terms: -2 + 2 = 0
2 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 7x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + 7x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 7x + x2 = 0 + -2
7x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
7x + x2 = -2

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 = -2 + 12.25

Reorder the terms:
12.25 + 7x + x2 = -2 + 12.25

Combine like terms: -2 + 12.25 = 10.25
12.25 + 7x + x2 = 10.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(x + 3.5) equal to 3.201562119 and -3.201562119.

Subproblem 1

x + 3.5 = 3.201562119 Simplifying x + 3.5 = 3.201562119 Reorder the terms: 3.5 + x = 3.201562119 Solving 3.5 + x = 3.201562119 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 = 3.201562119 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 3.201562119 + -3.5 x = 3.201562119 + -3.5 Combine like terms: 3.201562119 + -3.5 = -0.298437881 x = -0.298437881 Simplifying x = -0.298437881

Subproblem 2

x + 3.5 = -3.201562119 Simplifying x + 3.5 = -3.201562119 Reorder the terms: 3.5 + x = -3.201562119 Solving 3.5 + x = -3.201562119 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 = -3.201562119 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -3.201562119 + -3.5 x = -3.201562119 + -3.5 Combine like terms: -3.201562119 + -3.5 = -6.701562119 x = -6.701562119 Simplifying x = -6.701562119

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.298437881, -6.701562119}

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