8x^2-5x-30=0

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Solution for 8x^2-5x-30=0 equation:


Simplifying
8x2 + -5x + -30 = 0

Reorder the terms:
-30 + -5x + 8x2 = 0

Solving
-30 + -5x + 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'.
-3.75 + -0.625x + x2 = 0

Move the constant term to the right:

Add '3.75' to each side of the equation.
-3.75 + -0.625x + 3.75 + x2 = 0 + 3.75

Reorder the terms:
-3.75 + 3.75 + -0.625x + x2 = 0 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + -0.625x + x2 = 0 + 3.75
-0.625x + x2 = 0 + 3.75

Combine like terms: 0 + 3.75 = 3.75
-0.625x + x2 = 3.75

The x term is -0.625x.  Take half its coefficient (-0.3125).
Square it (0.09765625) and add it to both sides.

Add '0.09765625' to each side of the equation.
-0.625x + 0.09765625 + x2 = 3.75 + 0.09765625

Reorder the terms:
0.09765625 + -0.625x + x2 = 3.75 + 0.09765625

Combine like terms: 3.75 + 0.09765625 = 3.84765625
0.09765625 + -0.625x + x2 = 3.84765625

Factor a perfect square on the left side:
(x + -0.3125)(x + -0.3125) = 3.84765625

Calculate the square root of the right side: 1.961544353

Break this problem into two subproblems by setting 
(x + -0.3125) equal to 1.961544353 and -1.961544353.

Subproblem 1

x + -0.3125 = 1.961544353 Simplifying x + -0.3125 = 1.961544353 Reorder the terms: -0.3125 + x = 1.961544353 Solving -0.3125 + x = 1.961544353 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = 1.961544353 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = 1.961544353 + 0.3125 x = 1.961544353 + 0.3125 Combine like terms: 1.961544353 + 0.3125 = 2.274044353 x = 2.274044353 Simplifying x = 2.274044353

Subproblem 2

x + -0.3125 = -1.961544353 Simplifying x + -0.3125 = -1.961544353 Reorder the terms: -0.3125 + x = -1.961544353 Solving -0.3125 + x = -1.961544353 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = -1.961544353 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = -1.961544353 + 0.3125 x = -1.961544353 + 0.3125 Combine like terms: -1.961544353 + 0.3125 = -1.649044353 x = -1.649044353 Simplifying x = -1.649044353

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.274044353, -1.649044353}

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