21x^2-10x-8=0

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Solution for 21x^2-10x-8=0 equation:


Simplifying
21x2 + -10x + -8 = 0

Reorder the terms:
-8 + -10x + 21x2 = 0

Solving
-8 + -10x + 21x2 = 0

Solving for variable 'x'.

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

Divide each side by '21'.
-0.380952381 + -0.4761904762x + x2 = 0

Move the constant term to the right:

Add '0.380952381' to each side of the equation.
-0.380952381 + -0.4761904762x + 0.380952381 + x2 = 0 + 0.380952381

Reorder the terms:
-0.380952381 + 0.380952381 + -0.4761904762x + x2 = 0 + 0.380952381

Combine like terms: -0.380952381 + 0.380952381 = 0.000000000
0.000000000 + -0.4761904762x + x2 = 0 + 0.380952381
-0.4761904762x + x2 = 0 + 0.380952381

Combine like terms: 0 + 0.380952381 = 0.380952381
-0.4761904762x + x2 = 0.380952381

The x term is -0.4761904762x.  Take half its coefficient (-0.2380952381).
Square it (0.05668934241) and add it to both sides.

Add '0.05668934241' to each side of the equation.
-0.4761904762x + 0.05668934241 + x2 = 0.380952381 + 0.05668934241

Reorder the terms:
0.05668934241 + -0.4761904762x + x2 = 0.380952381 + 0.05668934241

Combine like terms: 0.380952381 + 0.05668934241 = 0.43764172341
0.05668934241 + -0.4761904762x + x2 = 0.43764172341

Factor a perfect square on the left side:
(x + -0.2380952381)(x + -0.2380952381) = 0.43764172341

Calculate the square root of the right side: 0.661544952

Break this problem into two subproblems by setting 
(x + -0.2380952381) equal to 0.661544952 and -0.661544952.

Subproblem 1

x + -0.2380952381 = 0.661544952 Simplifying x + -0.2380952381 = 0.661544952 Reorder the terms: -0.2380952381 + x = 0.661544952 Solving -0.2380952381 + x = 0.661544952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2380952381' to each side of the equation. -0.2380952381 + 0.2380952381 + x = 0.661544952 + 0.2380952381 Combine like terms: -0.2380952381 + 0.2380952381 = 0.0000000000 0.0000000000 + x = 0.661544952 + 0.2380952381 x = 0.661544952 + 0.2380952381 Combine like terms: 0.661544952 + 0.2380952381 = 0.8996401901 x = 0.8996401901 Simplifying x = 0.8996401901

Subproblem 2

x + -0.2380952381 = -0.661544952 Simplifying x + -0.2380952381 = -0.661544952 Reorder the terms: -0.2380952381 + x = -0.661544952 Solving -0.2380952381 + x = -0.661544952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2380952381' to each side of the equation. -0.2380952381 + 0.2380952381 + x = -0.661544952 + 0.2380952381 Combine like terms: -0.2380952381 + 0.2380952381 = 0.0000000000 0.0000000000 + x = -0.661544952 + 0.2380952381 x = -0.661544952 + 0.2380952381 Combine like terms: -0.661544952 + 0.2380952381 = -0.4234497139 x = -0.4234497139 Simplifying x = -0.4234497139

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.8996401901, -0.4234497139}

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