48x^2+46x-5=0

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Solution for 48x^2+46x-5=0 equation:


Simplifying
48x2 + 46x + -5 = 0

Reorder the terms:
-5 + 46x + 48x2 = 0

Solving
-5 + 46x + 48x2 = 0

Solving for variable 'x'.

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

Divide each side by '48'.
-0.1041666667 + 0.9583333333x + x2 = 0

Move the constant term to the right:

Add '0.1041666667' to each side of the equation.
-0.1041666667 + 0.9583333333x + 0.1041666667 + x2 = 0 + 0.1041666667

Reorder the terms:
-0.1041666667 + 0.1041666667 + 0.9583333333x + x2 = 0 + 0.1041666667

Combine like terms: -0.1041666667 + 0.1041666667 = 0.0000000000
0.0000000000 + 0.9583333333x + x2 = 0 + 0.1041666667
0.9583333333x + x2 = 0 + 0.1041666667

Combine like terms: 0 + 0.1041666667 = 0.1041666667
0.9583333333x + x2 = 0.1041666667

The x term is 0.9583333333x.  Take half its coefficient (0.4791666667).
Square it (0.2296006945) and add it to both sides.

Add '0.2296006945' to each side of the equation.
0.9583333333x + 0.2296006945 + x2 = 0.1041666667 + 0.2296006945

Reorder the terms:
0.2296006945 + 0.9583333333x + x2 = 0.1041666667 + 0.2296006945

Combine like terms: 0.1041666667 + 0.2296006945 = 0.3337673612
0.2296006945 + 0.9583333333x + x2 = 0.3337673612

Factor a perfect square on the left side:
(x + 0.4791666667)(x + 0.4791666667) = 0.3337673612

Calculate the square root of the right side: 0.577726026

Break this problem into two subproblems by setting 
(x + 0.4791666667) equal to 0.577726026 and -0.577726026.

Subproblem 1

x + 0.4791666667 = 0.577726026 Simplifying x + 0.4791666667 = 0.577726026 Reorder the terms: 0.4791666667 + x = 0.577726026 Solving 0.4791666667 + x = 0.577726026 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4791666667' to each side of the equation. 0.4791666667 + -0.4791666667 + x = 0.577726026 + -0.4791666667 Combine like terms: 0.4791666667 + -0.4791666667 = 0.0000000000 0.0000000000 + x = 0.577726026 + -0.4791666667 x = 0.577726026 + -0.4791666667 Combine like terms: 0.577726026 + -0.4791666667 = 0.0985593593 x = 0.0985593593 Simplifying x = 0.0985593593

Subproblem 2

x + 0.4791666667 = -0.577726026 Simplifying x + 0.4791666667 = -0.577726026 Reorder the terms: 0.4791666667 + x = -0.577726026 Solving 0.4791666667 + x = -0.577726026 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4791666667' to each side of the equation. 0.4791666667 + -0.4791666667 + x = -0.577726026 + -0.4791666667 Combine like terms: 0.4791666667 + -0.4791666667 = 0.0000000000 0.0000000000 + x = -0.577726026 + -0.4791666667 x = -0.577726026 + -0.4791666667 Combine like terms: -0.577726026 + -0.4791666667 = -1.0568926927 x = -1.0568926927 Simplifying x = -1.0568926927

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.0985593593, -1.0568926927}

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