8x^2-39x-45=0

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Solution for 8x^2-39x-45=0 equation:


Simplifying
8x2 + -39x + -45 = 0

Reorder the terms:
-45 + -39x + 8x2 = 0

Solving
-45 + -39x + 8x2 = 0

Solving for variable 'x'.

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

Divide each side by '8'.
-5.625 + -4.875x + x2 = 0

Move the constant term to the right:

Add '5.625' to each side of the equation.
-5.625 + -4.875x + 5.625 + x2 = 0 + 5.625

Reorder the terms:
-5.625 + 5.625 + -4.875x + x2 = 0 + 5.625

Combine like terms: -5.625 + 5.625 = 0.000
0.000 + -4.875x + x2 = 0 + 5.625
-4.875x + x2 = 0 + 5.625

Combine like terms: 0 + 5.625 = 5.625
-4.875x + x2 = 5.625

The x term is -4.875x.  Take half its coefficient (-2.4375).
Square it (5.94140625) and add it to both sides.

Add '5.94140625' to each side of the equation.
-4.875x + 5.94140625 + x2 = 5.625 + 5.94140625

Reorder the terms:
5.94140625 + -4.875x + x2 = 5.625 + 5.94140625

Combine like terms: 5.625 + 5.94140625 = 11.56640625
5.94140625 + -4.875x + x2 = 11.56640625

Factor a perfect square on the left side:
(x + -2.4375)(x + -2.4375) = 11.56640625

Calculate the square root of the right side: 3.400941965

Break this problem into two subproblems by setting 
(x + -2.4375) equal to 3.400941965 and -3.400941965.

Subproblem 1

x + -2.4375 = 3.400941965 Simplifying x + -2.4375 = 3.400941965 Reorder the terms: -2.4375 + x = 3.400941965 Solving -2.4375 + x = 3.400941965 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.4375' to each side of the equation. -2.4375 + 2.4375 + x = 3.400941965 + 2.4375 Combine like terms: -2.4375 + 2.4375 = 0.0000 0.0000 + x = 3.400941965 + 2.4375 x = 3.400941965 + 2.4375 Combine like terms: 3.400941965 + 2.4375 = 5.838441965 x = 5.838441965 Simplifying x = 5.838441965

Subproblem 2

x + -2.4375 = -3.400941965 Simplifying x + -2.4375 = -3.400941965 Reorder the terms: -2.4375 + x = -3.400941965 Solving -2.4375 + x = -3.400941965 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.4375' to each side of the equation. -2.4375 + 2.4375 + x = -3.400941965 + 2.4375 Combine like terms: -2.4375 + 2.4375 = 0.0000 0.0000 + x = -3.400941965 + 2.4375 x = -3.400941965 + 2.4375 Combine like terms: -3.400941965 + 2.4375 = -0.963441965 x = -0.963441965 Simplifying x = -0.963441965

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.838441965, -0.963441965}

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