1+3x=8x^2

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Solution for 1+3x=8x^2 equation:


Simplifying
1 + 3x = 8x2

Solving
1 + 3x = 8x2

Solving for variable 'x'.

Combine like terms: 8x2 + -8x2 = 0
1 + 3x + -8x2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-0.125 + -0.375x + x2 = 0

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + -0.375x + 0.125 + x2 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + -0.375x + x2 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + -0.375x + x2 = 0 + 0.125
-0.375x + x2 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
-0.375x + x2 = 0.125

The x term is -0.375x.  Take half its coefficient (-0.1875).
Square it (0.03515625) and add it to both sides.

Add '0.03515625' to each side of the equation.
-0.375x + 0.03515625 + x2 = 0.125 + 0.03515625

Reorder the terms:
0.03515625 + -0.375x + x2 = 0.125 + 0.03515625

Combine like terms: 0.125 + 0.03515625 = 0.16015625
0.03515625 + -0.375x + x2 = 0.16015625

Factor a perfect square on the left side:
(x + -0.1875)(x + -0.1875) = 0.16015625

Calculate the square root of the right side: 0.400195265

Break this problem into two subproblems by setting 
(x + -0.1875) equal to 0.400195265 and -0.400195265.

Subproblem 1

x + -0.1875 = 0.400195265 Simplifying x + -0.1875 = 0.400195265 Reorder the terms: -0.1875 + x = 0.400195265 Solving -0.1875 + x = 0.400195265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = 0.400195265 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = 0.400195265 + 0.1875 x = 0.400195265 + 0.1875 Combine like terms: 0.400195265 + 0.1875 = 0.587695265 x = 0.587695265 Simplifying x = 0.587695265

Subproblem 2

x + -0.1875 = -0.400195265 Simplifying x + -0.1875 = -0.400195265 Reorder the terms: -0.1875 + x = -0.400195265 Solving -0.1875 + x = -0.400195265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = -0.400195265 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = -0.400195265 + 0.1875 x = -0.400195265 + 0.1875 Combine like terms: -0.400195265 + 0.1875 = -0.212695265 x = -0.212695265 Simplifying x = -0.212695265

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.587695265, -0.212695265}

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