0=x^2+8x+4

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Solution for 0=x^2+8x+4 equation:


Simplifying
0 = x2 + 8x + 4

Reorder the terms:
0 = 4 + 8x + x2

Solving
0 = 4 + 8x + x2

Solving for variable 'x'.

Combine like terms: 0 + -4 = -4
-4 + -8x + -1x2 = 4 + 8x + x2 + -4 + -8x + -1x2

Reorder the terms:
-4 + -8x + -1x2 = 4 + -4 + 8x + -8x + x2 + -1x2

Combine like terms: 4 + -4 = 0
-4 + -8x + -1x2 = 0 + 8x + -8x + x2 + -1x2
-4 + -8x + -1x2 = 8x + -8x + x2 + -1x2

Combine like terms: 8x + -8x = 0
-4 + -8x + -1x2 = 0 + x2 + -1x2
-4 + -8x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-4 + -8x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(4 + 8x + x2) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(4 + 8x + x2)' equal to zero and attempt to solve: Simplifying 4 + 8x + x2 = 0 Solving 4 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 8x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 8x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 8x + x2 = 0 + -4 8x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 8x + x2 = -4 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 = -4 + 16 Reorder the terms: 16 + 8x + x2 = -4 + 16 Combine like terms: -4 + 16 = 12 16 + 8x + x2 = 12 Factor a perfect square on the left side: (x + 4)(x + 4) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (x + 4) equal to 3.464101615 and -3.464101615.

Subproblem 1

x + 4 = 3.464101615 Simplifying x + 4 = 3.464101615 Reorder the terms: 4 + x = 3.464101615 Solving 4 + x = 3.464101615 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 = 3.464101615 + -4 Combine like terms: 4 + -4 = 0 0 + x = 3.464101615 + -4 x = 3.464101615 + -4 Combine like terms: 3.464101615 + -4 = -0.535898385 x = -0.535898385 Simplifying x = -0.535898385

Subproblem 2

x + 4 = -3.464101615 Simplifying x + 4 = -3.464101615 Reorder the terms: 4 + x = -3.464101615 Solving 4 + x = -3.464101615 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 = -3.464101615 + -4 Combine like terms: 4 + -4 = 0 0 + x = -3.464101615 + -4 x = -3.464101615 + -4 Combine like terms: -3.464101615 + -4 = -7.464101615 x = -7.464101615 Simplifying x = -7.464101615

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.535898385, -7.464101615}

Solution

x = {-0.535898385, -7.464101615}

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