16x^2+49x+36=0

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Solution for 16x^2+49x+36=0 equation:


Simplifying
16x2 + 49x + 36 = 0

Reorder the terms:
36 + 49x + 16x2 = 0

Solving
36 + 49x + 16x2 = 0

Solving for variable 'x'.

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

Divide each side by '16'.
2.25 + 3.0625x + x2 = 0

Move the constant term to the right:

Add '-2.25' to each side of the equation.
2.25 + 3.0625x + -2.25 + x2 = 0 + -2.25

Reorder the terms:
2.25 + -2.25 + 3.0625x + x2 = 0 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + 3.0625x + x2 = 0 + -2.25
3.0625x + x2 = 0 + -2.25

Combine like terms: 0 + -2.25 = -2.25
3.0625x + x2 = -2.25

The x term is 3.0625x.  Take half its coefficient (1.53125).
Square it (2.344726563) and add it to both sides.

Add '2.344726563' to each side of the equation.
3.0625x + 2.344726563 + x2 = -2.25 + 2.344726563

Reorder the terms:
2.344726563 + 3.0625x + x2 = -2.25 + 2.344726563

Combine like terms: -2.25 + 2.344726563 = 0.094726563
2.344726563 + 3.0625x + x2 = 0.094726563

Factor a perfect square on the left side:
(x + 1.53125)(x + 1.53125) = 0.094726563

Calculate the square root of the right side: 0.307776807

Break this problem into two subproblems by setting 
(x + 1.53125) equal to 0.307776807 and -0.307776807.

Subproblem 1

x + 1.53125 = 0.307776807 Simplifying x + 1.53125 = 0.307776807 Reorder the terms: 1.53125 + x = 0.307776807 Solving 1.53125 + x = 0.307776807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.53125' to each side of the equation. 1.53125 + -1.53125 + x = 0.307776807 + -1.53125 Combine like terms: 1.53125 + -1.53125 = 0.00000 0.00000 + x = 0.307776807 + -1.53125 x = 0.307776807 + -1.53125 Combine like terms: 0.307776807 + -1.53125 = -1.223473193 x = -1.223473193 Simplifying x = -1.223473193

Subproblem 2

x + 1.53125 = -0.307776807 Simplifying x + 1.53125 = -0.307776807 Reorder the terms: 1.53125 + x = -0.307776807 Solving 1.53125 + x = -0.307776807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.53125' to each side of the equation. 1.53125 + -1.53125 + x = -0.307776807 + -1.53125 Combine like terms: 1.53125 + -1.53125 = 0.00000 0.00000 + x = -0.307776807 + -1.53125 x = -0.307776807 + -1.53125 Combine like terms: -0.307776807 + -1.53125 = -1.839026807 x = -1.839026807 Simplifying x = -1.839026807

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.223473193, -1.839026807}

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