0=x^2+20x+4

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Solution for 0=x^2+20x+4 equation:


Simplifying
0 = x2 + 20x + 4

Reorder the terms:
0 = 4 + 20x + x2

Solving
0 = 4 + 20x + x2

Solving for variable 'x'.

Combine like terms: 0 + -4 = -4
-4 + -20x + -1x2 = 4 + 20x + x2 + -4 + -20x + -1x2

Reorder the terms:
-4 + -20x + -1x2 = 4 + -4 + 20x + -20x + x2 + -1x2

Combine like terms: 4 + -4 = 0
-4 + -20x + -1x2 = 0 + 20x + -20x + x2 + -1x2
-4 + -20x + -1x2 = 20x + -20x + x2 + -1x2

Combine like terms: 20x + -20x = 0
-4 + -20x + -1x2 = 0 + x2 + -1x2
-4 + -20x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-4 + -20x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(4 + 20x + x2) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(4 + 20x + x2)' equal to zero and attempt to solve: Simplifying 4 + 20x + x2 = 0 Solving 4 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 20x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 20x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 20x + x2 = 0 + -4 20x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 20x + x2 = -4 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = -4 + 100 Reorder the terms: 100 + 20x + x2 = -4 + 100 Combine like terms: -4 + 100 = 96 100 + 20x + x2 = 96 Factor a perfect square on the left side: (x + 10)(x + 10) = 96 Calculate the square root of the right side: 9.797958971 Break this problem into two subproblems by setting (x + 10) equal to 9.797958971 and -9.797958971.

Subproblem 1

x + 10 = 9.797958971 Simplifying x + 10 = 9.797958971 Reorder the terms: 10 + x = 9.797958971 Solving 10 + x = 9.797958971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 9.797958971 + -10 Combine like terms: 10 + -10 = 0 0 + x = 9.797958971 + -10 x = 9.797958971 + -10 Combine like terms: 9.797958971 + -10 = -0.202041029 x = -0.202041029 Simplifying x = -0.202041029

Subproblem 2

x + 10 = -9.797958971 Simplifying x + 10 = -9.797958971 Reorder the terms: 10 + x = -9.797958971 Solving 10 + x = -9.797958971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -9.797958971 + -10 Combine like terms: 10 + -10 = 0 0 + x = -9.797958971 + -10 x = -9.797958971 + -10 Combine like terms: -9.797958971 + -10 = -19.797958971 x = -19.797958971 Simplifying x = -19.797958971

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.202041029, -19.797958971}

Solution

x = {-0.202041029, -19.797958971}

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