4x^2+49x-120=0

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Solution for 4x^2+49x-120=0 equation:


Simplifying
4x2 + 49x + -120 = 0

Reorder the terms:
-120 + 49x + 4x2 = 0

Solving
-120 + 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'.
-30 + 12.25x + x2 = 0

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 12.25x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + 12.25x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 12.25x + x2 = 0 + 30
12.25x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
12.25x + x2 = 30

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 = 30 + 37.515625

Reorder the terms:
37.515625 + 12.25x + x2 = 30 + 37.515625

Combine like terms: 30 + 37.515625 = 67.515625
37.515625 + 12.25x + x2 = 67.515625

Factor a perfect square on the left side:
(x + 6.125)(x + 6.125) = 67.515625

Calculate the square root of the right side: 8.216789215

Break this problem into two subproblems by setting 
(x + 6.125) equal to 8.216789215 and -8.216789215.

Subproblem 1

x + 6.125 = 8.216789215 Simplifying x + 6.125 = 8.216789215 Reorder the terms: 6.125 + x = 8.216789215 Solving 6.125 + x = 8.216789215 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 = 8.216789215 + -6.125 Combine like terms: 6.125 + -6.125 = 0.000 0.000 + x = 8.216789215 + -6.125 x = 8.216789215 + -6.125 Combine like terms: 8.216789215 + -6.125 = 2.091789215 x = 2.091789215 Simplifying x = 2.091789215

Subproblem 2

x + 6.125 = -8.216789215 Simplifying x + 6.125 = -8.216789215 Reorder the terms: 6.125 + x = -8.216789215 Solving 6.125 + x = -8.216789215 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 = -8.216789215 + -6.125 Combine like terms: 6.125 + -6.125 = 0.000 0.000 + x = -8.216789215 + -6.125 x = -8.216789215 + -6.125 Combine like terms: -8.216789215 + -6.125 = -14.341789215 x = -14.341789215 Simplifying x = -14.341789215

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.091789215, -14.341789215}

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