9x^2-16x+16=24x+17

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Solution for 9x^2-16x+16=24x+17 equation:


Simplifying
9x2 + -16x + 16 = 24x + 17

Reorder the terms:
16 + -16x + 9x2 = 24x + 17

Reorder the terms:
16 + -16x + 9x2 = 17 + 24x

Solving
16 + -16x + 9x2 = 17 + 24x

Solving for variable 'x'.

Reorder the terms:
16 + -17 + -16x + -24x + 9x2 = 17 + 24x + -17 + -24x

Combine like terms: 16 + -17 = -1
-1 + -16x + -24x + 9x2 = 17 + 24x + -17 + -24x

Combine like terms: -16x + -24x = -40x
-1 + -40x + 9x2 = 17 + 24x + -17 + -24x

Reorder the terms:
-1 + -40x + 9x2 = 17 + -17 + 24x + -24x

Combine like terms: 17 + -17 = 0
-1 + -40x + 9x2 = 0 + 24x + -24x
-1 + -40x + 9x2 = 24x + -24x

Combine like terms: 24x + -24x = 0
-1 + -40x + 9x2 = 0

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

Divide each side by '9'.
-0.1111111111 + -4.444444444x + x2 = 0

Move the constant term to the right:

Add '0.1111111111' to each side of the equation.
-0.1111111111 + -4.444444444x + 0.1111111111 + x2 = 0 + 0.1111111111

Reorder the terms:
-0.1111111111 + 0.1111111111 + -4.444444444x + x2 = 0 + 0.1111111111

Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000
0.0000000000 + -4.444444444x + x2 = 0 + 0.1111111111
-4.444444444x + x2 = 0 + 0.1111111111

Combine like terms: 0 + 0.1111111111 = 0.1111111111
-4.444444444x + x2 = 0.1111111111

The x term is -4.444444444x.  Take half its coefficient (-2.222222222).
Square it (4.938271604) and add it to both sides.

Add '4.938271604' to each side of the equation.
-4.444444444x + 4.938271604 + x2 = 0.1111111111 + 4.938271604

Reorder the terms:
4.938271604 + -4.444444444x + x2 = 0.1111111111 + 4.938271604

Combine like terms: 0.1111111111 + 4.938271604 = 5.0493827151
4.938271604 + -4.444444444x + x2 = 5.0493827151

Factor a perfect square on the left side:
(x + -2.222222222)(x + -2.222222222) = 5.0493827151

Calculate the square root of the right side: 2.247083157

Break this problem into two subproblems by setting 
(x + -2.222222222) equal to 2.247083157 and -2.247083157.

Subproblem 1

x + -2.222222222 = 2.247083157 Simplifying x + -2.222222222 = 2.247083157 Reorder the terms: -2.222222222 + x = 2.247083157 Solving -2.222222222 + x = 2.247083157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.222222222' to each side of the equation. -2.222222222 + 2.222222222 + x = 2.247083157 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + x = 2.247083157 + 2.222222222 x = 2.247083157 + 2.222222222 Combine like terms: 2.247083157 + 2.222222222 = 4.469305379 x = 4.469305379 Simplifying x = 4.469305379

Subproblem 2

x + -2.222222222 = -2.247083157 Simplifying x + -2.222222222 = -2.247083157 Reorder the terms: -2.222222222 + x = -2.247083157 Solving -2.222222222 + x = -2.247083157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.222222222' to each side of the equation. -2.222222222 + 2.222222222 + x = -2.247083157 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + x = -2.247083157 + 2.222222222 x = -2.247083157 + 2.222222222 Combine like terms: -2.247083157 + 2.222222222 = -0.024860935 x = -0.024860935 Simplifying x = -0.024860935

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.469305379, -0.024860935}

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