x=5x^2-3

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Solution for x=5x^2-3 equation:


Simplifying
x = 5x2 + -3

Reorder the terms:
x = -3 + 5x2

Solving
x = -3 + 5x2

Solving for variable 'x'.

Reorder the terms:
3 + x + -5x2 = -3 + 5x2 + 3 + -5x2

Reorder the terms:
3 + x + -5x2 = -3 + 3 + 5x2 + -5x2

Combine like terms: -3 + 3 = 0
3 + x + -5x2 = 0 + 5x2 + -5x2
3 + x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
3 + x + -5x2 = 0

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

Divide each side by '-5'.
-0.6 + -0.2x + x2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + -0.2x + 0.6 + x2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + -0.2x + x2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + -0.2x + x2 = 0 + 0.6
-0.2x + x2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
-0.2x + x2 = 0.6

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.
-0.2x + 0.25 + x2 = 0.6 + 0.25

Reorder the terms:
0.25 + -0.2x + x2 = 0.6 + 0.25

Combine like terms: 0.6 + 0.25 = 0.85
0.25 + -0.2x + x2 = 0.85

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.85

Calculate the square root of the right side: 0.921954446

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.921954446 and -0.921954446.

Subproblem 1

x + 0.5 = 0.921954446 Simplifying x + 0.5 = 0.921954446 Reorder the terms: 0.5 + x = 0.921954446 Solving 0.5 + x = 0.921954446 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 = 0.921954446 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.921954446 + -0.5 x = 0.921954446 + -0.5 Combine like terms: 0.921954446 + -0.5 = 0.421954446 x = 0.421954446 Simplifying x = 0.421954446

Subproblem 2

x + 0.5 = -0.921954446 Simplifying x + 0.5 = -0.921954446 Reorder the terms: 0.5 + x = -0.921954446 Solving 0.5 + x = -0.921954446 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 = -0.921954446 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.921954446 + -0.5 x = -0.921954446 + -0.5 Combine like terms: -0.921954446 + -0.5 = -1.421954446 x = -1.421954446 Simplifying x = -1.421954446

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.421954446, -1.421954446}

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