-.3x^2+2.7x+7=0

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Solution for -.3x^2+2.7x+7=0 equation:


Simplifying
-0.3x2 + 2.7x + 7 = 0

Reorder the terms:
7 + 2.7x + -0.3x2 = 0

Solving
7 + 2.7x + -0.3x2 = 0

Solving for variable 'x'.

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

Divide each side by '-0.3'.
-23.33333333 + -9x + x2 = 0

Move the constant term to the right:

Add '23.33333333' to each side of the equation.
-23.33333333 + -9x + 23.33333333 + x2 = 0 + 23.33333333

Reorder the terms:
-23.33333333 + 23.33333333 + -9x + x2 = 0 + 23.33333333

Combine like terms: -23.33333333 + 23.33333333 = 0.00000000
0.00000000 + -9x + x2 = 0 + 23.33333333
-9x + x2 = 0 + 23.33333333

Combine like terms: 0 + 23.33333333 = 23.33333333
-9x + x2 = 23.33333333

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = 23.33333333 + 20.25

Reorder the terms:
20.25 + -9x + x2 = 23.33333333 + 20.25

Combine like terms: 23.33333333 + 20.25 = 43.58333333
20.25 + -9x + x2 = 43.58333333

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 43.58333333

Calculate the square root of the right side: 6.60176744

Break this problem into two subproblems by setting 
(x + -4.5) equal to 6.60176744 and -6.60176744.

Subproblem 1

x + -4.5 = 6.60176744 Simplifying x + -4.5 = 6.60176744 Reorder the terms: -4.5 + x = 6.60176744 Solving -4.5 + x = 6.60176744 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 6.60176744 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 6.60176744 + 4.5 x = 6.60176744 + 4.5 Combine like terms: 6.60176744 + 4.5 = 11.10176744 x = 11.10176744 Simplifying x = 11.10176744

Subproblem 2

x + -4.5 = -6.60176744 Simplifying x + -4.5 = -6.60176744 Reorder the terms: -4.5 + x = -6.60176744 Solving -4.5 + x = -6.60176744 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -6.60176744 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -6.60176744 + 4.5 x = -6.60176744 + 4.5 Combine like terms: -6.60176744 + 4.5 = -2.10176744 x = -2.10176744 Simplifying x = -2.10176744

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.10176744, -2.10176744}

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