8x=5x^2-2

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Solution for 8x=5x^2-2 equation:


Simplifying
8x = 5x2 + -2

Reorder the terms:
8x = -2 + 5x2

Solving
8x = -2 + 5x2

Solving for variable 'x'.

Reorder the terms:
2 + 8x + -5x2 = -2 + 5x2 + 2 + -5x2

Reorder the terms:
2 + 8x + -5x2 = -2 + 2 + 5x2 + -5x2

Combine like terms: -2 + 2 = 0
2 + 8x + -5x2 = 0 + 5x2 + -5x2
2 + 8x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
2 + 8x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-0.4 + -1.6x + x2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + -1.6x + 0.4 + x2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + -1.6x + x2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + -1.6x + x2 = 0 + 0.4
-1.6x + x2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
-1.6x + x2 = 0.4

The x term is -1.6x.  Take half its coefficient (-0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
-1.6x + 0.64 + x2 = 0.4 + 0.64

Reorder the terms:
0.64 + -1.6x + x2 = 0.4 + 0.64

Combine like terms: 0.4 + 0.64 = 1.04
0.64 + -1.6x + x2 = 1.04

Factor a perfect square on the left side:
(x + -0.8)(x + -0.8) = 1.04

Calculate the square root of the right side: 1.019803903

Break this problem into two subproblems by setting 
(x + -0.8) equal to 1.019803903 and -1.019803903.

Subproblem 1

x + -0.8 = 1.019803903 Simplifying x + -0.8 = 1.019803903 Reorder the terms: -0.8 + x = 1.019803903 Solving -0.8 + x = 1.019803903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = 1.019803903 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 1.019803903 + 0.8 x = 1.019803903 + 0.8 Combine like terms: 1.019803903 + 0.8 = 1.819803903 x = 1.819803903 Simplifying x = 1.819803903

Subproblem 2

x + -0.8 = -1.019803903 Simplifying x + -0.8 = -1.019803903 Reorder the terms: -0.8 + x = -1.019803903 Solving -0.8 + x = -1.019803903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = -1.019803903 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -1.019803903 + 0.8 x = -1.019803903 + 0.8 Combine like terms: -1.019803903 + 0.8 = -0.219803903 x = -0.219803903 Simplifying x = -0.219803903

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.819803903, -0.219803903}

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