5x^2-10x-126=0

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Solution for 5x^2-10x-126=0 equation:


Simplifying
5x2 + -10x + -126 = 0

Reorder the terms:
-126 + -10x + 5x2 = 0

Solving
-126 + -10x + 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'.
-25.2 + -2x + x2 = 0

Move the constant term to the right:

Add '25.2' to each side of the equation.
-25.2 + -2x + 25.2 + x2 = 0 + 25.2

Reorder the terms:
-25.2 + 25.2 + -2x + x2 = 0 + 25.2

Combine like terms: -25.2 + 25.2 = 0.0
0.0 + -2x + x2 = 0 + 25.2
-2x + x2 = 0 + 25.2

Combine like terms: 0 + 25.2 = 25.2
-2x + x2 = 25.2

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 = 25.2 + 1

Reorder the terms:
1 + -2x + x2 = 25.2 + 1

Combine like terms: 25.2 + 1 = 26.2
1 + -2x + x2 = 26.2

Factor a perfect square on the left side:
(x + -1)(x + -1) = 26.2

Calculate the square root of the right side: 5.118593557

Break this problem into two subproblems by setting 
(x + -1) equal to 5.118593557 and -5.118593557.

Subproblem 1

x + -1 = 5.118593557 Simplifying x + -1 = 5.118593557 Reorder the terms: -1 + x = 5.118593557 Solving -1 + x = 5.118593557 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 = 5.118593557 + 1 Combine like terms: -1 + 1 = 0 0 + x = 5.118593557 + 1 x = 5.118593557 + 1 Combine like terms: 5.118593557 + 1 = 6.118593557 x = 6.118593557 Simplifying x = 6.118593557

Subproblem 2

x + -1 = -5.118593557 Simplifying x + -1 = -5.118593557 Reorder the terms: -1 + x = -5.118593557 Solving -1 + x = -5.118593557 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 = -5.118593557 + 1 Combine like terms: -1 + 1 = 0 0 + x = -5.118593557 + 1 x = -5.118593557 + 1 Combine like terms: -5.118593557 + 1 = -4.118593557 x = -4.118593557 Simplifying x = -4.118593557

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.118593557, -4.118593557}

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