5x^2+2x-54=0

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Solution for 5x^2+2x-54=0 equation:


Simplifying
5x2 + 2x + -54 = 0

Reorder the terms:
-54 + 2x + 5x2 = 0

Solving
-54 + 2x + 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'.
-10.8 + 0.4x + x2 = 0

Move the constant term to the right:

Add '10.8' to each side of the equation.
-10.8 + 0.4x + 10.8 + x2 = 0 + 10.8

Reorder the terms:
-10.8 + 10.8 + 0.4x + x2 = 0 + 10.8

Combine like terms: -10.8 + 10.8 = 0.0
0.0 + 0.4x + x2 = 0 + 10.8
0.4x + x2 = 0 + 10.8

Combine like terms: 0 + 10.8 = 10.8
0.4x + x2 = 10.8

The x term is 0.4x.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4x + 0.04 + x2 = 10.8 + 0.04

Reorder the terms:
0.04 + 0.4x + x2 = 10.8 + 0.04

Combine like terms: 10.8 + 0.04 = 10.84
0.04 + 0.4x + x2 = 10.84

Factor a perfect square on the left side:
(x + 0.2)(x + 0.2) = 10.84

Calculate the square root of the right side: 3.292415527

Break this problem into two subproblems by setting 
(x + 0.2) equal to 3.292415527 and -3.292415527.

Subproblem 1

x + 0.2 = 3.292415527 Simplifying x + 0.2 = 3.292415527 Reorder the terms: 0.2 + x = 3.292415527 Solving 0.2 + x = 3.292415527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 3.292415527 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 3.292415527 + -0.2 x = 3.292415527 + -0.2 Combine like terms: 3.292415527 + -0.2 = 3.092415527 x = 3.092415527 Simplifying x = 3.092415527

Subproblem 2

x + 0.2 = -3.292415527 Simplifying x + 0.2 = -3.292415527 Reorder the terms: 0.2 + x = -3.292415527 Solving 0.2 + x = -3.292415527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -3.292415527 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -3.292415527 + -0.2 x = -3.292415527 + -0.2 Combine like terms: -3.292415527 + -0.2 = -3.492415527 x = -3.492415527 Simplifying x = -3.492415527

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.092415527, -3.492415527}

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