2x^2+16x=-7

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Solution for 2x^2+16x=-7 equation:


Simplifying
2x2 + 16x = -7

Reorder the terms:
16x + 2x2 = -7

Solving
16x + 2x2 = -7

Solving for variable 'x'.

Reorder the terms:
7 + 16x + 2x2 = -7 + 7

Combine like terms: -7 + 7 = 0
7 + 16x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
3.5 + 8x + x2 = 0

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + 8x + -3.5 + x2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + 8x + x2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + 8x + x2 = 0 + -3.5
8x + x2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
8x + x2 = -3.5

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = -3.5 + 16

Reorder the terms:
16 + 8x + x2 = -3.5 + 16

Combine like terms: -3.5 + 16 = 12.5
16 + 8x + x2 = 12.5

Factor a perfect square on the left side:
(x + 4)(x + 4) = 12.5

Calculate the square root of the right side: 3.535533906

Break this problem into two subproblems by setting 
(x + 4) equal to 3.535533906 and -3.535533906.

Subproblem 1

x + 4 = 3.535533906 Simplifying x + 4 = 3.535533906 Reorder the terms: 4 + x = 3.535533906 Solving 4 + x = 3.535533906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 3.535533906 + -4 Combine like terms: 4 + -4 = 0 0 + x = 3.535533906 + -4 x = 3.535533906 + -4 Combine like terms: 3.535533906 + -4 = -0.464466094 x = -0.464466094 Simplifying x = -0.464466094

Subproblem 2

x + 4 = -3.535533906 Simplifying x + 4 = -3.535533906 Reorder the terms: 4 + x = -3.535533906 Solving 4 + x = -3.535533906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -3.535533906 + -4 Combine like terms: 4 + -4 = 0 0 + x = -3.535533906 + -4 x = -3.535533906 + -4 Combine like terms: -3.535533906 + -4 = -7.535533906 x = -7.535533906 Simplifying x = -7.535533906

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.464466094, -7.535533906}

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