2x^2-15x-4=0

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Solution for 2x^2-15x-4=0 equation:


Simplifying
2x2 + -15x + -4 = 0

Reorder the terms:
-4 + -15x + 2x2 = 0

Solving
-4 + -15x + 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'.
-2 + -7.5x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -7.5x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -7.5x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -7.5x + x2 = 0 + 2
-7.5x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-7.5x + x2 = 2

The x term is -7.5x.  Take half its coefficient (-3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
-7.5x + 14.0625 + x2 = 2 + 14.0625

Reorder the terms:
14.0625 + -7.5x + x2 = 2 + 14.0625

Combine like terms: 2 + 14.0625 = 16.0625
14.0625 + -7.5x + x2 = 16.0625

Factor a perfect square on the left side:
(x + -3.75)(x + -3.75) = 16.0625

Calculate the square root of the right side: 4.007804885

Break this problem into two subproblems by setting 
(x + -3.75) equal to 4.007804885 and -4.007804885.

Subproblem 1

x + -3.75 = 4.007804885 Simplifying x + -3.75 = 4.007804885 Reorder the terms: -3.75 + x = 4.007804885 Solving -3.75 + x = 4.007804885 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = 4.007804885 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 4.007804885 + 3.75 x = 4.007804885 + 3.75 Combine like terms: 4.007804885 + 3.75 = 7.757804885 x = 7.757804885 Simplifying x = 7.757804885

Subproblem 2

x + -3.75 = -4.007804885 Simplifying x + -3.75 = -4.007804885 Reorder the terms: -3.75 + x = -4.007804885 Solving -3.75 + x = -4.007804885 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = -4.007804885 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -4.007804885 + 3.75 x = -4.007804885 + 3.75 Combine like terms: -4.007804885 + 3.75 = -0.257804885 x = -0.257804885 Simplifying x = -0.257804885

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.757804885, -0.257804885}

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