3x^2=20x-10

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Solution for 3x^2=20x-10 equation:


Simplifying
3x2 = 20x + -10

Reorder the terms:
3x2 = -10 + 20x

Solving
3x2 = -10 + 20x

Solving for variable 'x'.

Reorder the terms:
10 + -20x + 3x2 = -10 + 20x + 10 + -20x

Reorder the terms:
10 + -20x + 3x2 = -10 + 10 + 20x + -20x

Combine like terms: -10 + 10 = 0
10 + -20x + 3x2 = 0 + 20x + -20x
10 + -20x + 3x2 = 20x + -20x

Combine like terms: 20x + -20x = 0
10 + -20x + 3x2 = 0

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

Divide each side by '3'.
3.333333333 + -6.666666667x + x2 = 0

Move the constant term to the right:

Add '-3.333333333' to each side of the equation.
3.333333333 + -6.666666667x + -3.333333333 + x2 = 0 + -3.333333333

Reorder the terms:
3.333333333 + -3.333333333 + -6.666666667x + x2 = 0 + -3.333333333

Combine like terms: 3.333333333 + -3.333333333 = 0.000000000
0.000000000 + -6.666666667x + x2 = 0 + -3.333333333
-6.666666667x + x2 = 0 + -3.333333333

Combine like terms: 0 + -3.333333333 = -3.333333333
-6.666666667x + x2 = -3.333333333

The x term is -6.666666667x.  Take half its coefficient (-3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
-6.666666667x + 11.11111112 + x2 = -3.333333333 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667x + x2 = -3.333333333 + 11.11111112

Combine like terms: -3.333333333 + 11.11111112 = 7.777777787
11.11111112 + -6.666666667x + x2 = 7.777777787

Factor a perfect square on the left side:
(x + -3.333333334)(x + -3.333333334) = 7.777777787

Calculate the square root of the right side: 2.788866757

Break this problem into two subproblems by setting 
(x + -3.333333334) equal to 2.788866757 and -2.788866757.

Subproblem 1

x + -3.333333334 = 2.788866757 Simplifying x + -3.333333334 = 2.788866757 Reorder the terms: -3.333333334 + x = 2.788866757 Solving -3.333333334 + x = 2.788866757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.333333334' to each side of the equation. -3.333333334 + 3.333333334 + x = 2.788866757 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + x = 2.788866757 + 3.333333334 x = 2.788866757 + 3.333333334 Combine like terms: 2.788866757 + 3.333333334 = 6.122200091 x = 6.122200091 Simplifying x = 6.122200091

Subproblem 2

x + -3.333333334 = -2.788866757 Simplifying x + -3.333333334 = -2.788866757 Reorder the terms: -3.333333334 + x = -2.788866757 Solving -3.333333334 + x = -2.788866757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.333333334' to each side of the equation. -3.333333334 + 3.333333334 + x = -2.788866757 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + x = -2.788866757 + 3.333333334 x = -2.788866757 + 3.333333334 Combine like terms: -2.788866757 + 3.333333334 = 0.544466577 x = 0.544466577 Simplifying x = 0.544466577

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.122200091, 0.544466577}

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