-0.2x^2+12x-20=7

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Solution for -0.2x^2+12x-20=7 equation:


Simplifying
-0.2x2 + 12x + -20 = 7

Reorder the terms:
-20 + 12x + -0.2x2 = 7

Solving
-20 + 12x + -0.2x2 = 7

Solving for variable 'x'.

Reorder the terms:
-20 + -7 + 12x + -0.2x2 = 7 + -7

Combine like terms: -20 + -7 = -27
-27 + 12x + -0.2x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-27 + 12x + -0.2x2 = 0

Begin completing the square.  Divide all terms by
-0.2 the coefficient of the squared term: 

Divide each side by '-0.2'.
135 + -60x + x2 = 0

Move the constant term to the right:

Add '-135' to each side of the equation.
135 + -60x + -135 + x2 = 0 + -135

Reorder the terms:
135 + -135 + -60x + x2 = 0 + -135

Combine like terms: 135 + -135 = 0
0 + -60x + x2 = 0 + -135
-60x + x2 = 0 + -135

Combine like terms: 0 + -135 = -135
-60x + x2 = -135

The x term is -60x.  Take half its coefficient (-30).
Square it (900) and add it to both sides.

Add '900' to each side of the equation.
-60x + 900 + x2 = -135 + 900

Reorder the terms:
900 + -60x + x2 = -135 + 900

Combine like terms: -135 + 900 = 765
900 + -60x + x2 = 765

Factor a perfect square on the left side:
(x + -30)(x + -30) = 765

Calculate the square root of the right side: 27.658633372

Break this problem into two subproblems by setting 
(x + -30) equal to 27.658633372 and -27.658633372.

Subproblem 1

x + -30 = 27.658633372 Simplifying x + -30 = 27.658633372 Reorder the terms: -30 + x = 27.658633372 Solving -30 + x = 27.658633372 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = 27.658633372 + 30 Combine like terms: -30 + 30 = 0 0 + x = 27.658633372 + 30 x = 27.658633372 + 30 Combine like terms: 27.658633372 + 30 = 57.658633372 x = 57.658633372 Simplifying x = 57.658633372

Subproblem 2

x + -30 = -27.658633372 Simplifying x + -30 = -27.658633372 Reorder the terms: -30 + x = -27.658633372 Solving -30 + x = -27.658633372 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = -27.658633372 + 30 Combine like terms: -30 + 30 = 0 0 + x = -27.658633372 + 30 x = -27.658633372 + 30 Combine like terms: -27.658633372 + 30 = 2.341366628 x = 2.341366628 Simplifying x = 2.341366628

Solution

The solution to the problem is based on the solutions from the subproblems. x = {57.658633372, 2.341366628}

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