(x+7)(x+7)=-3x

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Solution for (x+7)(x+7)=-3x equation:


Simplifying
(x + 7)(x + 7) = -3x

Reorder the terms:
(7 + x)(x + 7) = -3x

Reorder the terms:
(7 + x)(7 + x) = -3x

Multiply (7 + x) * (7 + x)
(7(7 + x) + x(7 + x)) = -3x
((7 * 7 + x * 7) + x(7 + x)) = -3x
((49 + 7x) + x(7 + x)) = -3x
(49 + 7x + (7 * x + x * x)) = -3x
(49 + 7x + (7x + x2)) = -3x

Combine like terms: 7x + 7x = 14x
(49 + 14x + x2) = -3x

Solving
49 + 14x + x2 = -3x

Solving for variable 'x'.

Reorder the terms:
49 + 14x + 3x + x2 = -3x + 3x

Combine like terms: 14x + 3x = 17x
49 + 17x + x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
49 + 17x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-49' to each side of the equation.
49 + 17x + -49 + x2 = 0 + -49

Reorder the terms:
49 + -49 + 17x + x2 = 0 + -49

Combine like terms: 49 + -49 = 0
0 + 17x + x2 = 0 + -49
17x + x2 = 0 + -49

Combine like terms: 0 + -49 = -49
17x + x2 = -49

The x term is 17x.  Take half its coefficient (8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
17x + 72.25 + x2 = -49 + 72.25

Reorder the terms:
72.25 + 17x + x2 = -49 + 72.25

Combine like terms: -49 + 72.25 = 23.25
72.25 + 17x + x2 = 23.25

Factor a perfect square on the left side:
(x + 8.5)(x + 8.5) = 23.25

Calculate the square root of the right side: 4.82182538

Break this problem into two subproblems by setting 
(x + 8.5) equal to 4.82182538 and -4.82182538.

Subproblem 1

x + 8.5 = 4.82182538 Simplifying x + 8.5 = 4.82182538 Reorder the terms: 8.5 + x = 4.82182538 Solving 8.5 + x = 4.82182538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = 4.82182538 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 4.82182538 + -8.5 x = 4.82182538 + -8.5 Combine like terms: 4.82182538 + -8.5 = -3.67817462 x = -3.67817462 Simplifying x = -3.67817462

Subproblem 2

x + 8.5 = -4.82182538 Simplifying x + 8.5 = -4.82182538 Reorder the terms: 8.5 + x = -4.82182538 Solving 8.5 + x = -4.82182538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = -4.82182538 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -4.82182538 + -8.5 x = -4.82182538 + -8.5 Combine like terms: -4.82182538 + -8.5 = -13.32182538 x = -13.32182538 Simplifying x = -13.32182538

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-3.67817462, -13.32182538}

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