21x^2-14x-100=0

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Solution for 21x^2-14x-100=0 equation:


Simplifying
21x2 + -14x + -100 = 0

Reorder the terms:
-100 + -14x + 21x2 = 0

Solving
-100 + -14x + 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'.
-4.761904762 + -0.6666666667x + x2 = 0

Move the constant term to the right:

Add '4.761904762' to each side of the equation.
-4.761904762 + -0.6666666667x + 4.761904762 + x2 = 0 + 4.761904762

Reorder the terms:
-4.761904762 + 4.761904762 + -0.6666666667x + x2 = 0 + 4.761904762

Combine like terms: -4.761904762 + 4.761904762 = 0.000000000
0.000000000 + -0.6666666667x + x2 = 0 + 4.761904762
-0.6666666667x + x2 = 0 + 4.761904762

Combine like terms: 0 + 4.761904762 = 4.761904762
-0.6666666667x + x2 = 4.761904762

The x term is -0.6666666667x.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667x + 0.1111111112 + x2 = 4.761904762 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = 4.761904762 + 0.1111111112

Combine like terms: 4.761904762 + 0.1111111112 = 4.8730158732
0.1111111112 + -0.6666666667x + x2 = 4.8730158732

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = 4.8730158732

Calculate the square root of the right side: 2.207490855

Break this problem into two subproblems by setting 
(x + -0.3333333334) equal to 2.207490855 and -2.207490855.

Subproblem 1

x + -0.3333333334 = 2.207490855 Simplifying x + -0.3333333334 = 2.207490855 Reorder the terms: -0.3333333334 + x = 2.207490855 Solving -0.3333333334 + x = 2.207490855 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = 2.207490855 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 2.207490855 + 0.3333333334 x = 2.207490855 + 0.3333333334 Combine like terms: 2.207490855 + 0.3333333334 = 2.5408241884 x = 2.5408241884 Simplifying x = 2.5408241884

Subproblem 2

x + -0.3333333334 = -2.207490855 Simplifying x + -0.3333333334 = -2.207490855 Reorder the terms: -0.3333333334 + x = -2.207490855 Solving -0.3333333334 + x = -2.207490855 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = -2.207490855 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -2.207490855 + 0.3333333334 x = -2.207490855 + 0.3333333334 Combine like terms: -2.207490855 + 0.3333333334 = -1.8741575216 x = -1.8741575216 Simplifying x = -1.8741575216

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.5408241884, -1.8741575216}

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