16x^2+3x-55=

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Solution for 16x^2+3x-55= equation:


Simplifying
16x2 + 3x + -55 = 0

Reorder the terms:
-55 + 3x + 16x2 = 0

Solving
-55 + 3x + 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'.
-3.4375 + 0.1875x + x2 = 0

Move the constant term to the right:

Add '3.4375' to each side of the equation.
-3.4375 + 0.1875x + 3.4375 + x2 = 0 + 3.4375

Reorder the terms:
-3.4375 + 3.4375 + 0.1875x + x2 = 0 + 3.4375

Combine like terms: -3.4375 + 3.4375 = 0.0000
0.0000 + 0.1875x + x2 = 0 + 3.4375
0.1875x + x2 = 0 + 3.4375

Combine like terms: 0 + 3.4375 = 3.4375
0.1875x + x2 = 3.4375

The x term is 0.1875x.  Take half its coefficient (0.09375).
Square it (0.0087890625) and add it to both sides.

Add '0.0087890625' to each side of the equation.
0.1875x + 0.0087890625 + x2 = 3.4375 + 0.0087890625

Reorder the terms:
0.0087890625 + 0.1875x + x2 = 3.4375 + 0.0087890625

Combine like terms: 3.4375 + 0.0087890625 = 3.4462890625
0.0087890625 + 0.1875x + x2 = 3.4462890625

Factor a perfect square on the left side:
(x + 0.09375)(x + 0.09375) = 3.4462890625

Calculate the square root of the right side: 1.856418343

Break this problem into two subproblems by setting 
(x + 0.09375) equal to 1.856418343 and -1.856418343.

Subproblem 1

x + 0.09375 = 1.856418343 Simplifying x + 0.09375 = 1.856418343 Reorder the terms: 0.09375 + x = 1.856418343 Solving 0.09375 + x = 1.856418343 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.09375' to each side of the equation. 0.09375 + -0.09375 + x = 1.856418343 + -0.09375 Combine like terms: 0.09375 + -0.09375 = 0.00000 0.00000 + x = 1.856418343 + -0.09375 x = 1.856418343 + -0.09375 Combine like terms: 1.856418343 + -0.09375 = 1.762668343 x = 1.762668343 Simplifying x = 1.762668343

Subproblem 2

x + 0.09375 = -1.856418343 Simplifying x + 0.09375 = -1.856418343 Reorder the terms: 0.09375 + x = -1.856418343 Solving 0.09375 + x = -1.856418343 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.09375' to each side of the equation. 0.09375 + -0.09375 + x = -1.856418343 + -0.09375 Combine like terms: 0.09375 + -0.09375 = 0.00000 0.00000 + x = -1.856418343 + -0.09375 x = -1.856418343 + -0.09375 Combine like terms: -1.856418343 + -0.09375 = -1.950168343 x = -1.950168343 Simplifying x = -1.950168343

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.762668343, -1.950168343}

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