7x+3=-x^2

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Solution for 7x+3=-x^2 equation:


Simplifying
7x + 3 = -1x2

Reorder the terms:
3 + 7x = -1x2

Solving
3 + 7x = -1x2

Solving for variable 'x'.

Combine like terms: -1x2 + x2 = 0
3 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 7x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + 7x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 7x + x2 = 0 + -3
7x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
7x + x2 = -3

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 = -3 + 12.25

Reorder the terms:
12.25 + 7x + x2 = -3 + 12.25

Combine like terms: -3 + 12.25 = 9.25
12.25 + 7x + x2 = 9.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(x + 3.5) equal to 3.041381265 and -3.041381265.

Subproblem 1

x + 3.5 = 3.041381265 Simplifying x + 3.5 = 3.041381265 Reorder the terms: 3.5 + x = 3.041381265 Solving 3.5 + x = 3.041381265 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 = 3.041381265 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 3.041381265 + -3.5 x = 3.041381265 + -3.5 Combine like terms: 3.041381265 + -3.5 = -0.458618735 x = -0.458618735 Simplifying x = -0.458618735

Subproblem 2

x + 3.5 = -3.041381265 Simplifying x + 3.5 = -3.041381265 Reorder the terms: 3.5 + x = -3.041381265 Solving 3.5 + x = -3.041381265 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 = -3.041381265 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -3.041381265 + -3.5 x = -3.041381265 + -3.5 Combine like terms: -3.041381265 + -3.5 = -6.541381265 x = -6.541381265 Simplifying x = -6.541381265

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.458618735, -6.541381265}

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