2x^2-21x-30=0

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Solution for 2x^2-21x-30=0 equation:


Simplifying
2x2 + -21x + -30 = 0

Reorder the terms:
-30 + -21x + 2x2 = 0

Solving
-30 + -21x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-15 + -10.5x + x2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -10.5x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + -10.5x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -10.5x + x2 = 0 + 15
-10.5x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
-10.5x + x2 = 15

The x term is -10.5x.  Take half its coefficient (-5.25).
Square it (27.5625) and add it to both sides.

Add '27.5625' to each side of the equation.
-10.5x + 27.5625 + x2 = 15 + 27.5625

Reorder the terms:
27.5625 + -10.5x + x2 = 15 + 27.5625

Combine like terms: 15 + 27.5625 = 42.5625
27.5625 + -10.5x + x2 = 42.5625

Factor a perfect square on the left side:
(x + -5.25)(x + -5.25) = 42.5625

Calculate the square root of the right side: 6.523994175

Break this problem into two subproblems by setting 
(x + -5.25) equal to 6.523994175 and -6.523994175.

Subproblem 1

x + -5.25 = 6.523994175 Simplifying x + -5.25 = 6.523994175 Reorder the terms: -5.25 + x = 6.523994175 Solving -5.25 + x = 6.523994175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = 6.523994175 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = 6.523994175 + 5.25 x = 6.523994175 + 5.25 Combine like terms: 6.523994175 + 5.25 = 11.773994175 x = 11.773994175 Simplifying x = 11.773994175

Subproblem 2

x + -5.25 = -6.523994175 Simplifying x + -5.25 = -6.523994175 Reorder the terms: -5.25 + x = -6.523994175 Solving -5.25 + x = -6.523994175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = -6.523994175 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = -6.523994175 + 5.25 x = -6.523994175 + 5.25 Combine like terms: -6.523994175 + 5.25 = -1.273994175 x = -1.273994175 Simplifying x = -1.273994175

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.773994175, -1.273994175}

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