24x^2+2x=3

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Solution for 24x^2+2x=3 equation:


Simplifying
24x2 + 2x = 3

Reorder the terms:
2x + 24x2 = 3

Solving
2x + 24x2 = 3

Solving for variable 'x'.

Reorder the terms:
-3 + 2x + 24x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 2x + 24x2 = 0

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

Divide each side by '24'.
-0.125 + 0.08333333333x + x2 = 0

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + 0.08333333333x + 0.125 + x2 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + 0.08333333333x + x2 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + 0.08333333333x + x2 = 0 + 0.125
0.08333333333x + x2 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
0.08333333333x + x2 = 0.125

The x term is 0.08333333333x.  Take half its coefficient (0.04166666667).
Square it (0.001736111111) and add it to both sides.

Add '0.001736111111' to each side of the equation.
0.08333333333x + 0.001736111111 + x2 = 0.125 + 0.001736111111

Reorder the terms:
0.001736111111 + 0.08333333333x + x2 = 0.125 + 0.001736111111

Combine like terms: 0.125 + 0.001736111111 = 0.126736111111
0.001736111111 + 0.08333333333x + x2 = 0.126736111111

Factor a perfect square on the left side:
(x + 0.04166666667)(x + 0.04166666667) = 0.126736111111

Calculate the square root of the right side: 0.356000156

Break this problem into two subproblems by setting 
(x + 0.04166666667) equal to 0.356000156 and -0.356000156.

Subproblem 1

x + 0.04166666667 = 0.356000156 Simplifying x + 0.04166666667 = 0.356000156 Reorder the terms: 0.04166666667 + x = 0.356000156 Solving 0.04166666667 + x = 0.356000156 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04166666667' to each side of the equation. 0.04166666667 + -0.04166666667 + x = 0.356000156 + -0.04166666667 Combine like terms: 0.04166666667 + -0.04166666667 = 0.00000000000 0.00000000000 + x = 0.356000156 + -0.04166666667 x = 0.356000156 + -0.04166666667 Combine like terms: 0.356000156 + -0.04166666667 = 0.31433348933 x = 0.31433348933 Simplifying x = 0.31433348933

Subproblem 2

x + 0.04166666667 = -0.356000156 Simplifying x + 0.04166666667 = -0.356000156 Reorder the terms: 0.04166666667 + x = -0.356000156 Solving 0.04166666667 + x = -0.356000156 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04166666667' to each side of the equation. 0.04166666667 + -0.04166666667 + x = -0.356000156 + -0.04166666667 Combine like terms: 0.04166666667 + -0.04166666667 = 0.00000000000 0.00000000000 + x = -0.356000156 + -0.04166666667 x = -0.356000156 + -0.04166666667 Combine like terms: -0.356000156 + -0.04166666667 = -0.39766682267 x = -0.39766682267 Simplifying x = -0.39766682267

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.31433348933, -0.39766682267}

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