19=7+29x-16x^2

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Solution for 19=7+29x-16x^2 equation:


Simplifying
19 = 7 + 29x + -16x2

Solving
19 = 7 + 29x + -16x2

Solving for variable 'x'.

Combine like terms: 19 + -7 = 12
12 + -29x + 16x2 = 7 + 29x + -16x2 + -7 + -29x + 16x2

Reorder the terms:
12 + -29x + 16x2 = 7 + -7 + 29x + -29x + -16x2 + 16x2

Combine like terms: 7 + -7 = 0
12 + -29x + 16x2 = 0 + 29x + -29x + -16x2 + 16x2
12 + -29x + 16x2 = 29x + -29x + -16x2 + 16x2

Combine like terms: 29x + -29x = 0
12 + -29x + 16x2 = 0 + -16x2 + 16x2
12 + -29x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
12 + -29x + 16x2 = 0

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

Divide each side by '16'.
0.75 + -1.8125x + x2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + -1.8125x + -0.75 + x2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + -1.8125x + x2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + -1.8125x + x2 = 0 + -0.75
-1.8125x + x2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
-1.8125x + x2 = -0.75

The x term is -1.8125x.  Take half its coefficient (-0.90625).
Square it (0.8212890625) and add it to both sides.

Add '0.8212890625' to each side of the equation.
-1.8125x + 0.8212890625 + x2 = -0.75 + 0.8212890625

Reorder the terms:
0.8212890625 + -1.8125x + x2 = -0.75 + 0.8212890625

Combine like terms: -0.75 + 0.8212890625 = 0.0712890625
0.8212890625 + -1.8125x + x2 = 0.0712890625

Factor a perfect square on the left side:
(x + -0.90625)(x + -0.90625) = 0.0712890625

Calculate the square root of the right side: 0.267000117

Break this problem into two subproblems by setting 
(x + -0.90625) equal to 0.267000117 and -0.267000117.

Subproblem 1

x + -0.90625 = 0.267000117 Simplifying x + -0.90625 = 0.267000117 Reorder the terms: -0.90625 + x = 0.267000117 Solving -0.90625 + x = 0.267000117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.90625' to each side of the equation. -0.90625 + 0.90625 + x = 0.267000117 + 0.90625 Combine like terms: -0.90625 + 0.90625 = 0.00000 0.00000 + x = 0.267000117 + 0.90625 x = 0.267000117 + 0.90625 Combine like terms: 0.267000117 + 0.90625 = 1.173250117 x = 1.173250117 Simplifying x = 1.173250117

Subproblem 2

x + -0.90625 = -0.267000117 Simplifying x + -0.90625 = -0.267000117 Reorder the terms: -0.90625 + x = -0.267000117 Solving -0.90625 + x = -0.267000117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.90625' to each side of the equation. -0.90625 + 0.90625 + x = -0.267000117 + 0.90625 Combine like terms: -0.90625 + 0.90625 = 0.00000 0.00000 + x = -0.267000117 + 0.90625 x = -0.267000117 + 0.90625 Combine like terms: -0.267000117 + 0.90625 = 0.639249883 x = 0.639249883 Simplifying x = 0.639249883

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.173250117, 0.639249883}

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