20x^2-63x-21=0

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Solution for 20x^2-63x-21=0 equation:


Simplifying
20x2 + -63x + -21 = 0

Reorder the terms:
-21 + -63x + 20x2 = 0

Solving
-21 + -63x + 20x2 = 0

Solving for variable 'x'.

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

Divide each side by '20'.
-1.05 + -3.15x + x2 = 0

Move the constant term to the right:

Add '1.05' to each side of the equation.
-1.05 + -3.15x + 1.05 + x2 = 0 + 1.05

Reorder the terms:
-1.05 + 1.05 + -3.15x + x2 = 0 + 1.05

Combine like terms: -1.05 + 1.05 = 0.00
0.00 + -3.15x + x2 = 0 + 1.05
-3.15x + x2 = 0 + 1.05

Combine like terms: 0 + 1.05 = 1.05
-3.15x + x2 = 1.05

The x term is -3.15x.  Take half its coefficient (-1.575).
Square it (2.480625) and add it to both sides.

Add '2.480625' to each side of the equation.
-3.15x + 2.480625 + x2 = 1.05 + 2.480625

Reorder the terms:
2.480625 + -3.15x + x2 = 1.05 + 2.480625

Combine like terms: 1.05 + 2.480625 = 3.530625
2.480625 + -3.15x + x2 = 3.530625

Factor a perfect square on the left side:
(x + -1.575)(x + -1.575) = 3.530625

Calculate the square root of the right side: 1.878995742

Break this problem into two subproblems by setting 
(x + -1.575) equal to 1.878995742 and -1.878995742.

Subproblem 1

x + -1.575 = 1.878995742 Simplifying x + -1.575 = 1.878995742 Reorder the terms: -1.575 + x = 1.878995742 Solving -1.575 + x = 1.878995742 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.575' to each side of the equation. -1.575 + 1.575 + x = 1.878995742 + 1.575 Combine like terms: -1.575 + 1.575 = 0.000 0.000 + x = 1.878995742 + 1.575 x = 1.878995742 + 1.575 Combine like terms: 1.878995742 + 1.575 = 3.453995742 x = 3.453995742 Simplifying x = 3.453995742

Subproblem 2

x + -1.575 = -1.878995742 Simplifying x + -1.575 = -1.878995742 Reorder the terms: -1.575 + x = -1.878995742 Solving -1.575 + x = -1.878995742 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.575' to each side of the equation. -1.575 + 1.575 + x = -1.878995742 + 1.575 Combine like terms: -1.575 + 1.575 = 0.000 0.000 + x = -1.878995742 + 1.575 x = -1.878995742 + 1.575 Combine like terms: -1.878995742 + 1.575 = -0.303995742 x = -0.303995742 Simplifying x = -0.303995742

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.453995742, -0.303995742}

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