4x^2-49x-900=0

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Solution for 4x^2-49x-900=0 equation:


Simplifying
4x2 + -49x + -900 = 0

Reorder the terms:
-900 + -49x + 4x2 = 0

Solving
-900 + -49x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-225 + -12.25x + x2 = 0

Move the constant term to the right:

Add '225' to each side of the equation.
-225 + -12.25x + 225 + x2 = 0 + 225

Reorder the terms:
-225 + 225 + -12.25x + x2 = 0 + 225

Combine like terms: -225 + 225 = 0
0 + -12.25x + x2 = 0 + 225
-12.25x + x2 = 0 + 225

Combine like terms: 0 + 225 = 225
-12.25x + x2 = 225

The x term is -12.25x.  Take half its coefficient (-6.125).
Square it (37.515625) and add it to both sides.

Add '37.515625' to each side of the equation.
-12.25x + 37.515625 + x2 = 225 + 37.515625

Reorder the terms:
37.515625 + -12.25x + x2 = 225 + 37.515625

Combine like terms: 225 + 37.515625 = 262.515625
37.515625 + -12.25x + x2 = 262.515625

Factor a perfect square on the left side:
(x + -6.125)(x + -6.125) = 262.515625

Calculate the square root of the right side: 16.202333937

Break this problem into two subproblems by setting 
(x + -6.125) equal to 16.202333937 and -16.202333937.

Subproblem 1

x + -6.125 = 16.202333937 Simplifying x + -6.125 = 16.202333937 Reorder the terms: -6.125 + x = 16.202333937 Solving -6.125 + x = 16.202333937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.125' to each side of the equation. -6.125 + 6.125 + x = 16.202333937 + 6.125 Combine like terms: -6.125 + 6.125 = 0.000 0.000 + x = 16.202333937 + 6.125 x = 16.202333937 + 6.125 Combine like terms: 16.202333937 + 6.125 = 22.327333937 x = 22.327333937 Simplifying x = 22.327333937

Subproblem 2

x + -6.125 = -16.202333937 Simplifying x + -6.125 = -16.202333937 Reorder the terms: -6.125 + x = -16.202333937 Solving -6.125 + x = -16.202333937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.125' to each side of the equation. -6.125 + 6.125 + x = -16.202333937 + 6.125 Combine like terms: -6.125 + 6.125 = 0.000 0.000 + x = -16.202333937 + 6.125 x = -16.202333937 + 6.125 Combine like terms: -16.202333937 + 6.125 = -10.077333937 x = -10.077333937 Simplifying x = -10.077333937

Solution

The solution to the problem is based on the solutions from the subproblems. x = {22.327333937, -10.077333937}

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