20x^2+11x-48=0

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Solution for 20x^2+11x-48=0 equation:


Simplifying
20x2 + 11x + -48 = 0

Reorder the terms:
-48 + 11x + 20x2 = 0

Solving
-48 + 11x + 20x2 = 0

Solving for variable 'x'.

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

Divide each side by '20'.
-2.4 + 0.55x + x2 = 0

Move the constant term to the right:

Add '2.4' to each side of the equation.
-2.4 + 0.55x + 2.4 + x2 = 0 + 2.4

Reorder the terms:
-2.4 + 2.4 + 0.55x + x2 = 0 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + 0.55x + x2 = 0 + 2.4
0.55x + x2 = 0 + 2.4

Combine like terms: 0 + 2.4 = 2.4
0.55x + x2 = 2.4

The x term is 0.55x.  Take half its coefficient (0.275).
Square it (0.075625) and add it to both sides.

Add '0.075625' to each side of the equation.
0.55x + 0.075625 + x2 = 2.4 + 0.075625

Reorder the terms:
0.075625 + 0.55x + x2 = 2.4 + 0.075625

Combine like terms: 2.4 + 0.075625 = 2.475625
0.075625 + 0.55x + x2 = 2.475625

Factor a perfect square on the left side:
(x + 0.275)(x + 0.275) = 2.475625

Calculate the square root of the right side: 1.573411898

Break this problem into two subproblems by setting 
(x + 0.275) equal to 1.573411898 and -1.573411898.

Subproblem 1

x + 0.275 = 1.573411898 Simplifying x + 0.275 = 1.573411898 Reorder the terms: 0.275 + x = 1.573411898 Solving 0.275 + x = 1.573411898 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.275' to each side of the equation. 0.275 + -0.275 + x = 1.573411898 + -0.275 Combine like terms: 0.275 + -0.275 = 0.000 0.000 + x = 1.573411898 + -0.275 x = 1.573411898 + -0.275 Combine like terms: 1.573411898 + -0.275 = 1.298411898 x = 1.298411898 Simplifying x = 1.298411898

Subproblem 2

x + 0.275 = -1.573411898 Simplifying x + 0.275 = -1.573411898 Reorder the terms: 0.275 + x = -1.573411898 Solving 0.275 + x = -1.573411898 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.275' to each side of the equation. 0.275 + -0.275 + x = -1.573411898 + -0.275 Combine like terms: 0.275 + -0.275 = 0.000 0.000 + x = -1.573411898 + -0.275 x = -1.573411898 + -0.275 Combine like terms: -1.573411898 + -0.275 = -1.848411898 x = -1.848411898 Simplifying x = -1.848411898

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.298411898, -1.848411898}

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