16x^2+18x=19

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Solution for 16x^2+18x=19 equation:


Simplifying
16x2 + 18x = 19

Reorder the terms:
18x + 16x2 = 19

Solving
18x + 16x2 = 19

Solving for variable 'x'.

Reorder the terms:
-19 + 18x + 16x2 = 19 + -19

Combine like terms: 19 + -19 = 0
-19 + 18x + 16x2 = 0

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

Divide each side by '16'.
-1.1875 + 1.125x + x2 = 0

Move the constant term to the right:

Add '1.1875' to each side of the equation.
-1.1875 + 1.125x + 1.1875 + x2 = 0 + 1.1875

Reorder the terms:
-1.1875 + 1.1875 + 1.125x + x2 = 0 + 1.1875

Combine like terms: -1.1875 + 1.1875 = 0.0000
0.0000 + 1.125x + x2 = 0 + 1.1875
1.125x + x2 = 0 + 1.1875

Combine like terms: 0 + 1.1875 = 1.1875
1.125x + x2 = 1.1875

The x term is 1.125x.  Take half its coefficient (0.5625).
Square it (0.31640625) and add it to both sides.

Add '0.31640625' to each side of the equation.
1.125x + 0.31640625 + x2 = 1.1875 + 0.31640625

Reorder the terms:
0.31640625 + 1.125x + x2 = 1.1875 + 0.31640625

Combine like terms: 1.1875 + 0.31640625 = 1.50390625
0.31640625 + 1.125x + x2 = 1.50390625

Factor a perfect square on the left side:
(x + 0.5625)(x + 0.5625) = 1.50390625

Calculate the square root of the right side: 1.226338554

Break this problem into two subproblems by setting 
(x + 0.5625) equal to 1.226338554 and -1.226338554.

Subproblem 1

x + 0.5625 = 1.226338554 Simplifying x + 0.5625 = 1.226338554 Reorder the terms: 0.5625 + x = 1.226338554 Solving 0.5625 + x = 1.226338554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + x = 1.226338554 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = 1.226338554 + -0.5625 x = 1.226338554 + -0.5625 Combine like terms: 1.226338554 + -0.5625 = 0.663838554 x = 0.663838554 Simplifying x = 0.663838554

Subproblem 2

x + 0.5625 = -1.226338554 Simplifying x + 0.5625 = -1.226338554 Reorder the terms: 0.5625 + x = -1.226338554 Solving 0.5625 + x = -1.226338554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + x = -1.226338554 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = -1.226338554 + -0.5625 x = -1.226338554 + -0.5625 Combine like terms: -1.226338554 + -0.5625 = -1.788838554 x = -1.788838554 Simplifying x = -1.788838554

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.663838554, -1.788838554}

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