4x^2+120x+497=0

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Solution for 4x^2+120x+497=0 equation:


Simplifying
4x2 + 120x + 497 = 0

Reorder the terms:
497 + 120x + 4x2 = 0

Solving
497 + 120x + 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'.
124.25 + 30x + x2 = 0

Move the constant term to the right:

Add '-124.25' to each side of the equation.
124.25 + 30x + -124.25 + x2 = 0 + -124.25

Reorder the terms:
124.25 + -124.25 + 30x + x2 = 0 + -124.25

Combine like terms: 124.25 + -124.25 = 0.00
0.00 + 30x + x2 = 0 + -124.25
30x + x2 = 0 + -124.25

Combine like terms: 0 + -124.25 = -124.25
30x + x2 = -124.25

The x term is 30x.  Take half its coefficient (15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
30x + 225 + x2 = -124.25 + 225

Reorder the terms:
225 + 30x + x2 = -124.25 + 225

Combine like terms: -124.25 + 225 = 100.75
225 + 30x + x2 = 100.75

Factor a perfect square on the left side:
(x + 15)(x + 15) = 100.75

Calculate the square root of the right side: 10.03742995

Break this problem into two subproblems by setting 
(x + 15) equal to 10.03742995 and -10.03742995.

Subproblem 1

x + 15 = 10.03742995 Simplifying x + 15 = 10.03742995 Reorder the terms: 15 + x = 10.03742995 Solving 15 + x = 10.03742995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 10.03742995 + -15 Combine like terms: 15 + -15 = 0 0 + x = 10.03742995 + -15 x = 10.03742995 + -15 Combine like terms: 10.03742995 + -15 = -4.96257005 x = -4.96257005 Simplifying x = -4.96257005

Subproblem 2

x + 15 = -10.03742995 Simplifying x + 15 = -10.03742995 Reorder the terms: 15 + x = -10.03742995 Solving 15 + x = -10.03742995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -10.03742995 + -15 Combine like terms: 15 + -15 = 0 0 + x = -10.03742995 + -15 x = -10.03742995 + -15 Combine like terms: -10.03742995 + -15 = -25.03742995 x = -25.03742995 Simplifying x = -25.03742995

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-4.96257005, -25.03742995}

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