0=9+4x^2-16x

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Solution for 0=9+4x^2-16x equation:


Simplifying
0 = 9 + 4x2 + -16x

Reorder the terms:
0 = 9 + -16x + 4x2

Solving
0 = 9 + -16x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + -9 = -9
-9 + 16x + -4x2 = 9 + -16x + 4x2 + -9 + 16x + -4x2

Reorder the terms:
-9 + 16x + -4x2 = 9 + -9 + -16x + 16x + 4x2 + -4x2

Combine like terms: 9 + -9 = 0
-9 + 16x + -4x2 = 0 + -16x + 16x + 4x2 + -4x2
-9 + 16x + -4x2 = -16x + 16x + 4x2 + -4x2

Combine like terms: -16x + 16x = 0
-9 + 16x + -4x2 = 0 + 4x2 + -4x2
-9 + 16x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-9 + 16x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
2.25 + -4x + x2 = 0

Move the constant term to the right:

Add '-2.25' to each side of the equation.
2.25 + -4x + -2.25 + x2 = 0 + -2.25

Reorder the terms:
2.25 + -2.25 + -4x + x2 = 0 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + -4x + x2 = 0 + -2.25
-4x + x2 = 0 + -2.25

Combine like terms: 0 + -2.25 = -2.25
-4x + x2 = -2.25

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -2.25 + 4

Reorder the terms:
4 + -4x + x2 = -2.25 + 4

Combine like terms: -2.25 + 4 = 1.75
4 + -4x + x2 = 1.75

Factor a perfect square on the left side:
(x + -2)(x + -2) = 1.75

Calculate the square root of the right side: 1.322875656

Break this problem into two subproblems by setting 
(x + -2) equal to 1.322875656 and -1.322875656.

Subproblem 1

x + -2 = 1.322875656 Simplifying x + -2 = 1.322875656 Reorder the terms: -2 + x = 1.322875656 Solving -2 + x = 1.322875656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 1.322875656 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.322875656 + 2 x = 1.322875656 + 2 Combine like terms: 1.322875656 + 2 = 3.322875656 x = 3.322875656 Simplifying x = 3.322875656

Subproblem 2

x + -2 = -1.322875656 Simplifying x + -2 = -1.322875656 Reorder the terms: -2 + x = -1.322875656 Solving -2 + x = -1.322875656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -1.322875656 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.322875656 + 2 x = -1.322875656 + 2 Combine like terms: -1.322875656 + 2 = 0.677124344 x = 0.677124344 Simplifying x = 0.677124344

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.322875656, 0.677124344}

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