5X^2+6X-46=0

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Solution for 5X^2+6X-46=0 equation:


Simplifying
5X2 + 6X + -46 = 0

Reorder the terms:
-46 + 6X + 5X2 = 0

Solving
-46 + 6X + 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'.
-9.2 + 1.2X + X2 = 0

Move the constant term to the right:

Add '9.2' to each side of the equation.
-9.2 + 1.2X + 9.2 + X2 = 0 + 9.2

Reorder the terms:
-9.2 + 9.2 + 1.2X + X2 = 0 + 9.2

Combine like terms: -9.2 + 9.2 = 0.0
0.0 + 1.2X + X2 = 0 + 9.2
1.2X + X2 = 0 + 9.2

Combine like terms: 0 + 9.2 = 9.2
1.2X + X2 = 9.2

The X term is 1.2X.  Take half its coefficient (0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
1.2X + 0.36 + X2 = 9.2 + 0.36

Reorder the terms:
0.36 + 1.2X + X2 = 9.2 + 0.36

Combine like terms: 9.2 + 0.36 = 9.56
0.36 + 1.2X + X2 = 9.56

Factor a perfect square on the left side:
(X + 0.6)(X + 0.6) = 9.56

Calculate the square root of the right side: 3.091924967

Break this problem into two subproblems by setting 
(X + 0.6) equal to 3.091924967 and -3.091924967.

Subproblem 1

X + 0.6 = 3.091924967 Simplifying X + 0.6 = 3.091924967 Reorder the terms: 0.6 + X = 3.091924967 Solving 0.6 + X = 3.091924967 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + X = 3.091924967 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + X = 3.091924967 + -0.6 X = 3.091924967 + -0.6 Combine like terms: 3.091924967 + -0.6 = 2.491924967 X = 2.491924967 Simplifying X = 2.491924967

Subproblem 2

X + 0.6 = -3.091924967 Simplifying X + 0.6 = -3.091924967 Reorder the terms: 0.6 + X = -3.091924967 Solving 0.6 + X = -3.091924967 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + X = -3.091924967 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + X = -3.091924967 + -0.6 X = -3.091924967 + -0.6 Combine like terms: -3.091924967 + -0.6 = -3.691924967 X = -3.691924967 Simplifying X = -3.691924967

Solution

The solution to the problem is based on the solutions from the subproblems. X = {2.491924967, -3.691924967}

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