x+x^2-0.3=0

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Solution for x+x^2-0.3=0 equation:


Simplifying
x + x2 + -0.3 = 0

Reorder the terms:
-0.3 + x + x2 = 0

Solving
-0.3 + x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.3' to each side of the equation.
-0.3 + x + 0.3 + x2 = 0 + 0.3

Reorder the terms:
-0.3 + 0.3 + x + x2 = 0 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + x + x2 = 0 + 0.3
x + x2 = 0 + 0.3

Combine like terms: 0 + 0.3 = 0.3
x + x2 = 0.3

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.
x + 0.25 + x2 = 0.3 + 0.25

Reorder the terms:
0.25 + x + x2 = 0.3 + 0.25

Combine like terms: 0.3 + 0.25 = 0.55
0.25 + x + x2 = 0.55

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.55

Calculate the square root of the right side: 0.741619849

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.741619849 and -0.741619849.

Subproblem 1

x + 0.5 = 0.741619849 Simplifying x + 0.5 = 0.741619849 Reorder the terms: 0.5 + x = 0.741619849 Solving 0.5 + x = 0.741619849 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 = 0.741619849 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.741619849 + -0.5 x = 0.741619849 + -0.5 Combine like terms: 0.741619849 + -0.5 = 0.241619849 x = 0.241619849 Simplifying x = 0.241619849

Subproblem 2

x + 0.5 = -0.741619849 Simplifying x + 0.5 = -0.741619849 Reorder the terms: 0.5 + x = -0.741619849 Solving 0.5 + x = -0.741619849 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 = -0.741619849 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.741619849 + -0.5 x = -0.741619849 + -0.5 Combine like terms: -0.741619849 + -0.5 = -1.241619849 x = -1.241619849 Simplifying x = -1.241619849

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.241619849, -1.241619849}

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