9x^2-2x-38=0

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Solution for 9x^2-2x-38=0 equation:


Simplifying
9x2 + -2x + -38 = 0

Reorder the terms:
-38 + -2x + 9x2 = 0

Solving
-38 + -2x + 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'.
-4.222222222 + -0.2222222222x + x2 = 0

Move the constant term to the right:

Add '4.222222222' to each side of the equation.
-4.222222222 + -0.2222222222x + 4.222222222 + x2 = 0 + 4.222222222

Reorder the terms:
-4.222222222 + 4.222222222 + -0.2222222222x + x2 = 0 + 4.222222222

Combine like terms: -4.222222222 + 4.222222222 = 0.000000000
0.000000000 + -0.2222222222x + x2 = 0 + 4.222222222
-0.2222222222x + x2 = 0 + 4.222222222

Combine like terms: 0 + 4.222222222 = 4.222222222
-0.2222222222x + x2 = 4.222222222

The x term is -0.2222222222x.  Take half its coefficient (-0.1111111111).
Square it (0.01234567901) and add it to both sides.

Add '0.01234567901' to each side of the equation.
-0.2222222222x + 0.01234567901 + x2 = 4.222222222 + 0.01234567901

Reorder the terms:
0.01234567901 + -0.2222222222x + x2 = 4.222222222 + 0.01234567901

Combine like terms: 4.222222222 + 0.01234567901 = 4.23456790101
0.01234567901 + -0.2222222222x + x2 = 4.23456790101

Factor a perfect square on the left side:
(x + -0.1111111111)(x + -0.1111111111) = 4.23456790101

Calculate the square root of the right side: 2.057806575

Break this problem into two subproblems by setting 
(x + -0.1111111111) equal to 2.057806575 and -2.057806575.

Subproblem 1

x + -0.1111111111 = 2.057806575 Simplifying x + -0.1111111111 = 2.057806575 Reorder the terms: -0.1111111111 + x = 2.057806575 Solving -0.1111111111 + x = 2.057806575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + x = 2.057806575 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + x = 2.057806575 + 0.1111111111 x = 2.057806575 + 0.1111111111 Combine like terms: 2.057806575 + 0.1111111111 = 2.1689176861 x = 2.1689176861 Simplifying x = 2.1689176861

Subproblem 2

x + -0.1111111111 = -2.057806575 Simplifying x + -0.1111111111 = -2.057806575 Reorder the terms: -0.1111111111 + x = -2.057806575 Solving -0.1111111111 + x = -2.057806575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + x = -2.057806575 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + x = -2.057806575 + 0.1111111111 x = -2.057806575 + 0.1111111111 Combine like terms: -2.057806575 + 0.1111111111 = -1.9466954639 x = -1.9466954639 Simplifying x = -1.9466954639

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.1689176861, -1.9466954639}

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