5X^2+98X-98=0

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Solution for 5X^2+98X-98=0 equation:


Simplifying
5X2 + 98X + -98 = 0

Reorder the terms:
-98 + 98X + 5X2 = 0

Solving
-98 + 98X + 5X2 = 0

Solving for variable 'X'.

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

Divide each side by '5'.
-19.6 + 19.6X + X2 = 0

Move the constant term to the right:

Add '19.6' to each side of the equation.
-19.6 + 19.6X + 19.6 + X2 = 0 + 19.6

Reorder the terms:
-19.6 + 19.6 + 19.6X + X2 = 0 + 19.6

Combine like terms: -19.6 + 19.6 = 0.0
0.0 + 19.6X + X2 = 0 + 19.6
19.6X + X2 = 0 + 19.6

Combine like terms: 0 + 19.6 = 19.6
19.6X + X2 = 19.6

The X term is 19.6X.  Take half its coefficient (9.8).
Square it (96.04) and add it to both sides.

Add '96.04' to each side of the equation.
19.6X + 96.04 + X2 = 19.6 + 96.04

Reorder the terms:
96.04 + 19.6X + X2 = 19.6 + 96.04

Combine like terms: 19.6 + 96.04 = 115.64
96.04 + 19.6X + X2 = 115.64

Factor a perfect square on the left side:
(X + 9.8)(X + 9.8) = 115.64

Calculate the square root of the right side: 10.753604047

Break this problem into two subproblems by setting 
(X + 9.8) equal to 10.753604047 and -10.753604047.

Subproblem 1

X + 9.8 = 10.753604047 Simplifying X + 9.8 = 10.753604047 Reorder the terms: 9.8 + X = 10.753604047 Solving 9.8 + X = 10.753604047 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-9.8' to each side of the equation. 9.8 + -9.8 + X = 10.753604047 + -9.8 Combine like terms: 9.8 + -9.8 = 0.0 0.0 + X = 10.753604047 + -9.8 X = 10.753604047 + -9.8 Combine like terms: 10.753604047 + -9.8 = 0.953604047 X = 0.953604047 Simplifying X = 0.953604047

Subproblem 2

X + 9.8 = -10.753604047 Simplifying X + 9.8 = -10.753604047 Reorder the terms: 9.8 + X = -10.753604047 Solving 9.8 + X = -10.753604047 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-9.8' to each side of the equation. 9.8 + -9.8 + X = -10.753604047 + -9.8 Combine like terms: 9.8 + -9.8 = 0.0 0.0 + X = -10.753604047 + -9.8 X = -10.753604047 + -9.8 Combine like terms: -10.753604047 + -9.8 = -20.553604047 X = -20.553604047 Simplifying X = -20.553604047

Solution

The solution to the problem is based on the solutions from the subproblems. X = {0.953604047, -20.553604047}

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