.3x^2=1.8x+.3

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Solution for .3x^2=1.8x+.3 equation:


Simplifying
0.3x2 = 1.8x + 0.3

Reorder the terms:
0.3x2 = 0.3 + 1.8x

Solving
0.3x2 = 0.3 + 1.8x

Solving for variable 'x'.

Reorder the terms:
-0.3 + -1.8x + 0.3x2 = 0.3 + 1.8x + -0.3 + -1.8x

Reorder the terms:
-0.3 + -1.8x + 0.3x2 = 0.3 + -0.3 + 1.8x + -1.8x

Combine like terms: 0.3 + -0.3 = 0.0
-0.3 + -1.8x + 0.3x2 = 0.0 + 1.8x + -1.8x
-0.3 + -1.8x + 0.3x2 = 1.8x + -1.8x

Combine like terms: 1.8x + -1.8x = 0.0
-0.3 + -1.8x + 0.3x2 = 0.0

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

Divide each side by '0.3'.
-1 + -6x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -6x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -6x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -6x + x2 = 0 + 1
-6x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-6x + x2 = 1

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 1 + 9

Reorder the terms:
9 + -6x + x2 = 1 + 9

Combine like terms: 1 + 9 = 10
9 + -6x + x2 = 10

Factor a perfect square on the left side:
(x + -3)(x + -3) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(x + -3) equal to 3.16227766 and -3.16227766.

Subproblem 1

x + -3 = 3.16227766 Simplifying x + -3 = 3.16227766 Reorder the terms: -3 + x = 3.16227766 Solving -3 + x = 3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.16227766 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.16227766 + 3 x = 3.16227766 + 3 Combine like terms: 3.16227766 + 3 = 6.16227766 x = 6.16227766 Simplifying x = 6.16227766

Subproblem 2

x + -3 = -3.16227766 Simplifying x + -3 = -3.16227766 Reorder the terms: -3 + x = -3.16227766 Solving -3 + x = -3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.16227766 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.16227766 + 3 x = -3.16227766 + 3 Combine like terms: -3.16227766 + 3 = -0.16227766 x = -0.16227766 Simplifying x = -0.16227766

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.16227766, -0.16227766}

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