x(x)+20x+98=0

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Solution for x(x)+20x+98=0 equation:


Simplifying
x(x) + 20x + 98 = 0

Multiply x * x
x2 + 20x + 98 = 0

Reorder the terms:
98 + 20x + x2 = 0

Solving
98 + 20x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-98' to each side of the equation.
98 + 20x + -98 + x2 = 0 + -98

Reorder the terms:
98 + -98 + 20x + x2 = 0 + -98

Combine like terms: 98 + -98 = 0
0 + 20x + x2 = 0 + -98
20x + x2 = 0 + -98

Combine like terms: 0 + -98 = -98
20x + x2 = -98

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 = -98 + 100

Reorder the terms:
100 + 20x + x2 = -98 + 100

Combine like terms: -98 + 100 = 2
100 + 20x + x2 = 2

Factor a perfect square on the left side:
(x + 10)(x + 10) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(x + 10) equal to 1.414213562 and -1.414213562.

Subproblem 1

x + 10 = 1.414213562 Simplifying x + 10 = 1.414213562 Reorder the terms: 10 + x = 1.414213562 Solving 10 + x = 1.414213562 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 = 1.414213562 + -10 Combine like terms: 10 + -10 = 0 0 + x = 1.414213562 + -10 x = 1.414213562 + -10 Combine like terms: 1.414213562 + -10 = -8.585786438 x = -8.585786438 Simplifying x = -8.585786438

Subproblem 2

x + 10 = -1.414213562 Simplifying x + 10 = -1.414213562 Reorder the terms: 10 + x = -1.414213562 Solving 10 + x = -1.414213562 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 = -1.414213562 + -10 Combine like terms: 10 + -10 = 0 0 + x = -1.414213562 + -10 x = -1.414213562 + -10 Combine like terms: -1.414213562 + -10 = -11.414213562 x = -11.414213562 Simplifying x = -11.414213562

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-8.585786438, -11.414213562}

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