2x=5x^2-8

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


Simplifying
2x = 5x2 + -8

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

Solving
2x = -8 + 5x2

Solving for variable 'x'.

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

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

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

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

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

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

Move the constant term to the right:

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

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

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

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

The x term is -0.4x.  Take half its coefficient (-0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
-0.4x + 0.04 + x2 = 1.6 + 0.04

Reorder the terms:
0.04 + -0.4x + x2 = 1.6 + 0.04

Combine like terms: 1.6 + 0.04 = 1.64
0.04 + -0.4x + x2 = 1.64

Factor a perfect square on the left side:
(x + -0.2)(x + -0.2) = 1.64

Calculate the square root of the right side: 1.280624847

Break this problem into two subproblems by setting 
(x + -0.2) equal to 1.280624847 and -1.280624847.

Subproblem 1

x + -0.2 = 1.280624847 Simplifying x + -0.2 = 1.280624847 Reorder the terms: -0.2 + x = 1.280624847 Solving -0.2 + x = 1.280624847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 1.280624847 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 1.280624847 + 0.2 x = 1.280624847 + 0.2 Combine like terms: 1.280624847 + 0.2 = 1.480624847 x = 1.480624847 Simplifying x = 1.480624847

Subproblem 2

x + -0.2 = -1.280624847 Simplifying x + -0.2 = -1.280624847 Reorder the terms: -0.2 + x = -1.280624847 Solving -0.2 + x = -1.280624847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -1.280624847 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -1.280624847 + 0.2 x = -1.280624847 + 0.2 Combine like terms: -1.280624847 + 0.2 = -1.080624847 x = -1.080624847 Simplifying x = -1.080624847

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.480624847, -1.080624847}

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