21x^2+107x-18=0

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Solution for 21x^2+107x-18=0 equation:


Simplifying
21x2 + 107x + -18 = 0

Reorder the terms:
-18 + 107x + 21x2 = 0

Solving
-18 + 107x + 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'.
-0.8571428571 + 5.095238095x + x2 = 0

Move the constant term to the right:

Add '0.8571428571' to each side of the equation.
-0.8571428571 + 5.095238095x + 0.8571428571 + x2 = 0 + 0.8571428571

Reorder the terms:
-0.8571428571 + 0.8571428571 + 5.095238095x + x2 = 0 + 0.8571428571

Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000
0.0000000000 + 5.095238095x + x2 = 0 + 0.8571428571
5.095238095x + x2 = 0 + 0.8571428571

Combine like terms: 0 + 0.8571428571 = 0.8571428571
5.095238095x + x2 = 0.8571428571

The x term is 5.095238095x.  Take half its coefficient (2.547619048).
Square it (6.490362814) and add it to both sides.

Add '6.490362814' to each side of the equation.
5.095238095x + 6.490362814 + x2 = 0.8571428571 + 6.490362814

Reorder the terms:
6.490362814 + 5.095238095x + x2 = 0.8571428571 + 6.490362814

Combine like terms: 0.8571428571 + 6.490362814 = 7.3475056711
6.490362814 + 5.095238095x + x2 = 7.3475056711

Factor a perfect square on the left side:
(x + 2.547619048)(x + 2.547619048) = 7.3475056711

Calculate the square root of the right side: 2.71062828

Break this problem into two subproblems by setting 
(x + 2.547619048) equal to 2.71062828 and -2.71062828.

Subproblem 1

x + 2.547619048 = 2.71062828 Simplifying x + 2.547619048 = 2.71062828 Reorder the terms: 2.547619048 + x = 2.71062828 Solving 2.547619048 + x = 2.71062828 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.547619048' to each side of the equation. 2.547619048 + -2.547619048 + x = 2.71062828 + -2.547619048 Combine like terms: 2.547619048 + -2.547619048 = 0.000000000 0.000000000 + x = 2.71062828 + -2.547619048 x = 2.71062828 + -2.547619048 Combine like terms: 2.71062828 + -2.547619048 = 0.163009232 x = 0.163009232 Simplifying x = 0.163009232

Subproblem 2

x + 2.547619048 = -2.71062828 Simplifying x + 2.547619048 = -2.71062828 Reorder the terms: 2.547619048 + x = -2.71062828 Solving 2.547619048 + x = -2.71062828 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.547619048' to each side of the equation. 2.547619048 + -2.547619048 + x = -2.71062828 + -2.547619048 Combine like terms: 2.547619048 + -2.547619048 = 0.000000000 0.000000000 + x = -2.71062828 + -2.547619048 x = -2.71062828 + -2.547619048 Combine like terms: -2.71062828 + -2.547619048 = -5.258247328 x = -5.258247328 Simplifying x = -5.258247328

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.163009232, -5.258247328}

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