15x^2-44x+21=9

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Solution for 15x^2-44x+21=9 equation:


Simplifying
15x2 + -44x + 21 = 9

Reorder the terms:
21 + -44x + 15x2 = 9

Solving
21 + -44x + 15x2 = 9

Solving for variable 'x'.

Reorder the terms:
21 + -9 + -44x + 15x2 = 9 + -9

Combine like terms: 21 + -9 = 12
12 + -44x + 15x2 = 9 + -9

Combine like terms: 9 + -9 = 0
12 + -44x + 15x2 = 0

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

Divide each side by '15'.
0.8 + -2.933333333x + x2 = 0

Move the constant term to the right:

Add '-0.8' to each side of the equation.
0.8 + -2.933333333x + -0.8 + x2 = 0 + -0.8

Reorder the terms:
0.8 + -0.8 + -2.933333333x + x2 = 0 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + -2.933333333x + x2 = 0 + -0.8
-2.933333333x + x2 = 0 + -0.8

Combine like terms: 0 + -0.8 = -0.8
-2.933333333x + x2 = -0.8

The x term is -2.933333333x.  Take half its coefficient (-1.466666667).
Square it (2.151111112) and add it to both sides.

Add '2.151111112' to each side of the equation.
-2.933333333x + 2.151111112 + x2 = -0.8 + 2.151111112

Reorder the terms:
2.151111112 + -2.933333333x + x2 = -0.8 + 2.151111112

Combine like terms: -0.8 + 2.151111112 = 1.351111112
2.151111112 + -2.933333333x + x2 = 1.351111112

Factor a perfect square on the left side:
(x + -1.466666667)(x + -1.466666667) = 1.351111112

Calculate the square root of the right side: 1.162373052

Break this problem into two subproblems by setting 
(x + -1.466666667) equal to 1.162373052 and -1.162373052.

Subproblem 1

x + -1.466666667 = 1.162373052 Simplifying x + -1.466666667 = 1.162373052 Reorder the terms: -1.466666667 + x = 1.162373052 Solving -1.466666667 + x = 1.162373052 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.466666667' to each side of the equation. -1.466666667 + 1.466666667 + x = 1.162373052 + 1.466666667 Combine like terms: -1.466666667 + 1.466666667 = 0.000000000 0.000000000 + x = 1.162373052 + 1.466666667 x = 1.162373052 + 1.466666667 Combine like terms: 1.162373052 + 1.466666667 = 2.629039719 x = 2.629039719 Simplifying x = 2.629039719

Subproblem 2

x + -1.466666667 = -1.162373052 Simplifying x + -1.466666667 = -1.162373052 Reorder the terms: -1.466666667 + x = -1.162373052 Solving -1.466666667 + x = -1.162373052 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.466666667' to each side of the equation. -1.466666667 + 1.466666667 + x = -1.162373052 + 1.466666667 Combine like terms: -1.466666667 + 1.466666667 = 0.000000000 0.000000000 + x = -1.162373052 + 1.466666667 x = -1.162373052 + 1.466666667 Combine like terms: -1.162373052 + 1.466666667 = 0.304293615 x = 0.304293615 Simplifying x = 0.304293615

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.629039719, 0.304293615}

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