5x^2-8x-124=0

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Solution for 5x^2-8x-124=0 equation:


Simplifying
5x2 + -8x + -124 = 0

Reorder the terms:
-124 + -8x + 5x2 = 0

Solving
-124 + -8x + 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'.
-24.8 + -1.6x + x2 = 0

Move the constant term to the right:

Add '24.8' to each side of the equation.
-24.8 + -1.6x + 24.8 + x2 = 0 + 24.8

Reorder the terms:
-24.8 + 24.8 + -1.6x + x2 = 0 + 24.8

Combine like terms: -24.8 + 24.8 = 0.0
0.0 + -1.6x + x2 = 0 + 24.8
-1.6x + x2 = 0 + 24.8

Combine like terms: 0 + 24.8 = 24.8
-1.6x + x2 = 24.8

The x term is -1.6x.  Take half its coefficient (-0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
-1.6x + 0.64 + x2 = 24.8 + 0.64

Reorder the terms:
0.64 + -1.6x + x2 = 24.8 + 0.64

Combine like terms: 24.8 + 0.64 = 25.44
0.64 + -1.6x + x2 = 25.44

Factor a perfect square on the left side:
(x + -0.8)(x + -0.8) = 25.44

Calculate the square root of the right side: 5.043808085

Break this problem into two subproblems by setting 
(x + -0.8) equal to 5.043808085 and -5.043808085.

Subproblem 1

x + -0.8 = 5.043808085 Simplifying x + -0.8 = 5.043808085 Reorder the terms: -0.8 + x = 5.043808085 Solving -0.8 + x = 5.043808085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = 5.043808085 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 5.043808085 + 0.8 x = 5.043808085 + 0.8 Combine like terms: 5.043808085 + 0.8 = 5.843808085 x = 5.843808085 Simplifying x = 5.843808085

Subproblem 2

x + -0.8 = -5.043808085 Simplifying x + -0.8 = -5.043808085 Reorder the terms: -0.8 + x = -5.043808085 Solving -0.8 + x = -5.043808085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = -5.043808085 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -5.043808085 + 0.8 x = -5.043808085 + 0.8 Combine like terms: -5.043808085 + 0.8 = -4.243808085 x = -4.243808085 Simplifying x = -4.243808085

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.843808085, -4.243808085}

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