4x^2+196x+45=0

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Solution for 4x^2+196x+45=0 equation:


Simplifying
4x2 + 196x + 45 = 0

Reorder the terms:
45 + 196x + 4x2 = 0

Solving
45 + 196x + 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'.
11.25 + 49x + x2 = 0

Move the constant term to the right:

Add '-11.25' to each side of the equation.
11.25 + 49x + -11.25 + x2 = 0 + -11.25

Reorder the terms:
11.25 + -11.25 + 49x + x2 = 0 + -11.25

Combine like terms: 11.25 + -11.25 = 0.00
0.00 + 49x + x2 = 0 + -11.25
49x + x2 = 0 + -11.25

Combine like terms: 0 + -11.25 = -11.25
49x + x2 = -11.25

The x term is 49x.  Take half its coefficient (24.5).
Square it (600.25) and add it to both sides.

Add '600.25' to each side of the equation.
49x + 600.25 + x2 = -11.25 + 600.25

Reorder the terms:
600.25 + 49x + x2 = -11.25 + 600.25

Combine like terms: -11.25 + 600.25 = 589
600.25 + 49x + x2 = 589

Factor a perfect square on the left side:
(x + 24.5)(x + 24.5) = 589

Calculate the square root of the right side: 24.269322199

Break this problem into two subproblems by setting 
(x + 24.5) equal to 24.269322199 and -24.269322199.

Subproblem 1

x + 24.5 = 24.269322199 Simplifying x + 24.5 = 24.269322199 Reorder the terms: 24.5 + x = 24.269322199 Solving 24.5 + x = 24.269322199 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24.5' to each side of the equation. 24.5 + -24.5 + x = 24.269322199 + -24.5 Combine like terms: 24.5 + -24.5 = 0.0 0.0 + x = 24.269322199 + -24.5 x = 24.269322199 + -24.5 Combine like terms: 24.269322199 + -24.5 = -0.230677801 x = -0.230677801 Simplifying x = -0.230677801

Subproblem 2

x + 24.5 = -24.269322199 Simplifying x + 24.5 = -24.269322199 Reorder the terms: 24.5 + x = -24.269322199 Solving 24.5 + x = -24.269322199 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24.5' to each side of the equation. 24.5 + -24.5 + x = -24.269322199 + -24.5 Combine like terms: 24.5 + -24.5 = 0.0 0.0 + x = -24.269322199 + -24.5 x = -24.269322199 + -24.5 Combine like terms: -24.269322199 + -24.5 = -48.769322199 x = -48.769322199 Simplifying x = -48.769322199

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.230677801, -48.769322199}

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