9x^2-34x-21=0

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Solution for 9x^2-34x-21=0 equation:


Simplifying
9x2 + -34x + -21 = 0

Reorder the terms:
-21 + -34x + 9x2 = 0

Solving
-21 + -34x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
-2.333333333 + -3.777777778x + x2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + -3.777777778x + 2.333333333 + x2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + -3.777777778x + x2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + -3.777777778x + x2 = 0 + 2.333333333
-3.777777778x + x2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
-3.777777778x + x2 = 2.333333333

The x term is -3.777777778x.  Take half its coefficient (-1.888888889).
Square it (3.567901235) and add it to both sides.

Add '3.567901235' to each side of the equation.
-3.777777778x + 3.567901235 + x2 = 2.333333333 + 3.567901235

Reorder the terms:
3.567901235 + -3.777777778x + x2 = 2.333333333 + 3.567901235

Combine like terms: 2.333333333 + 3.567901235 = 5.901234568
3.567901235 + -3.777777778x + x2 = 5.901234568

Factor a perfect square on the left side:
(x + -1.888888889)(x + -1.888888889) = 5.901234568

Calculate the square root of the right side: 2.429245679

Break this problem into two subproblems by setting 
(x + -1.888888889) equal to 2.429245679 and -2.429245679.

Subproblem 1

x + -1.888888889 = 2.429245679 Simplifying x + -1.888888889 = 2.429245679 Reorder the terms: -1.888888889 + x = 2.429245679 Solving -1.888888889 + x = 2.429245679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.888888889' to each side of the equation. -1.888888889 + 1.888888889 + x = 2.429245679 + 1.888888889 Combine like terms: -1.888888889 + 1.888888889 = 0.000000000 0.000000000 + x = 2.429245679 + 1.888888889 x = 2.429245679 + 1.888888889 Combine like terms: 2.429245679 + 1.888888889 = 4.318134568 x = 4.318134568 Simplifying x = 4.318134568

Subproblem 2

x + -1.888888889 = -2.429245679 Simplifying x + -1.888888889 = -2.429245679 Reorder the terms: -1.888888889 + x = -2.429245679 Solving -1.888888889 + x = -2.429245679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.888888889' to each side of the equation. -1.888888889 + 1.888888889 + x = -2.429245679 + 1.888888889 Combine like terms: -1.888888889 + 1.888888889 = 0.000000000 0.000000000 + x = -2.429245679 + 1.888888889 x = -2.429245679 + 1.888888889 Combine like terms: -2.429245679 + 1.888888889 = -0.54035679 x = -0.54035679 Simplifying x = -0.54035679

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.318134568, -0.54035679}

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