8x^2=3-8x

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Solution for 8x^2=3-8x equation:


Simplifying
8x2 = 3 + -8x

Solving
8x2 = 3 + -8x

Solving for variable 'x'.

Reorder the terms:
-3 + 8x + 8x2 = 3 + -8x + -3 + 8x

Reorder the terms:
-3 + 8x + 8x2 = 3 + -3 + -8x + 8x

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

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

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

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

Move the constant term to the right:

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

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

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

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

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 0.375 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 0.375 + 0.25

Combine like terms: 0.375 + 0.25 = 0.625
1.25 + x2 = 0.625

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.625

Calculate the square root of the right side: 0.790569415

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.790569415 and -0.790569415.

Subproblem 1

x + 0.5 = 0.790569415 Simplifying x + 0.5 = 0.790569415 Reorder the terms: 0.5 + x = 0.790569415 Solving 0.5 + x = 0.790569415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.790569415 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.790569415 + -0.5 x = 0.790569415 + -0.5 Combine like terms: 0.790569415 + -0.5 = 0.290569415 x = 0.290569415 Simplifying x = 0.290569415

Subproblem 2

x + 0.5 = -0.790569415 Simplifying x + 0.5 = -0.790569415 Reorder the terms: 0.5 + x = -0.790569415 Solving 0.5 + x = -0.790569415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.790569415 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.790569415 + -0.5 x = -0.790569415 + -0.5 Combine like terms: -0.790569415 + -0.5 = -1.290569415 x = -1.290569415 Simplifying x = -1.290569415

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.290569415, -1.290569415}

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