4X^2-8X-273=0

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Solution for 4X^2-8X-273=0 equation:


Simplifying
4X2 + -8X + -273 = 0

Reorder the terms:
-273 + -8X + 4X2 = 0

Solving
-273 + -8X + 4X2 = 0

Solving for variable 'X'.

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

Divide each side by '4'.
-68.25 + -2X + X2 = 0

Move the constant term to the right:

Add '68.25' to each side of the equation.
-68.25 + -2X + 68.25 + X2 = 0 + 68.25

Reorder the terms:
-68.25 + 68.25 + -2X + X2 = 0 + 68.25

Combine like terms: -68.25 + 68.25 = 0.00
0.00 + -2X + X2 = 0 + 68.25
-2X + X2 = 0 + 68.25

Combine like terms: 0 + 68.25 = 68.25
-2X + X2 = 68.25

The X term is -2X.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2X + 1 + X2 = 68.25 + 1

Reorder the terms:
1 + -2X + X2 = 68.25 + 1

Combine like terms: 68.25 + 1 = 69.25
1 + -2X + X2 = 69.25

Factor a perfect square on the left side:
(X + -1)(X + -1) = 69.25

Calculate the square root of the right side: 8.321658489

Break this problem into two subproblems by setting 
(X + -1) equal to 8.321658489 and -8.321658489.

Subproblem 1

X + -1 = 8.321658489 Simplifying X + -1 = 8.321658489 Reorder the terms: -1 + X = 8.321658489 Solving -1 + X = 8.321658489 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + X = 8.321658489 + 1 Combine like terms: -1 + 1 = 0 0 + X = 8.321658489 + 1 X = 8.321658489 + 1 Combine like terms: 8.321658489 + 1 = 9.321658489 X = 9.321658489 Simplifying X = 9.321658489

Subproblem 2

X + -1 = -8.321658489 Simplifying X + -1 = -8.321658489 Reorder the terms: -1 + X = -8.321658489 Solving -1 + X = -8.321658489 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + X = -8.321658489 + 1 Combine like terms: -1 + 1 = 0 0 + X = -8.321658489 + 1 X = -8.321658489 + 1 Combine like terms: -8.321658489 + 1 = -7.321658489 X = -7.321658489 Simplifying X = -7.321658489

Solution

The solution to the problem is based on the solutions from the subproblems. X = {9.321658489, -7.321658489}

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