9x+8x^2=22

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Solution for 9x+8x^2=22 equation:


Simplifying
9x + 8x2 = 22

Solving
9x + 8x2 = 22

Solving for variable 'x'.

Reorder the terms:
-22 + 9x + 8x2 = 22 + -22

Combine like terms: 22 + -22 = 0
-22 + 9x + 8x2 = 0

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

Divide each side by '8'.
-2.75 + 1.125x + x2 = 0

Move the constant term to the right:

Add '2.75' to each side of the equation.
-2.75 + 1.125x + 2.75 + x2 = 0 + 2.75

Reorder the terms:
-2.75 + 2.75 + 1.125x + x2 = 0 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + 1.125x + x2 = 0 + 2.75
1.125x + x2 = 0 + 2.75

Combine like terms: 0 + 2.75 = 2.75
1.125x + x2 = 2.75

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 = 2.75 + 0.31640625

Reorder the terms:
0.31640625 + 1.125x + x2 = 2.75 + 0.31640625

Combine like terms: 2.75 + 0.31640625 = 3.06640625
0.31640625 + 1.125x + x2 = 3.06640625

Factor a perfect square on the left side:
(x + 0.5625)(x + 0.5625) = 3.06640625

Calculate the square root of the right side: 1.751115716

Break this problem into two subproblems by setting 
(x + 0.5625) equal to 1.751115716 and -1.751115716.

Subproblem 1

x + 0.5625 = 1.751115716 Simplifying x + 0.5625 = 1.751115716 Reorder the terms: 0.5625 + x = 1.751115716 Solving 0.5625 + x = 1.751115716 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 = 1.751115716 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = 1.751115716 + -0.5625 x = 1.751115716 + -0.5625 Combine like terms: 1.751115716 + -0.5625 = 1.188615716 x = 1.188615716 Simplifying x = 1.188615716

Subproblem 2

x + 0.5625 = -1.751115716 Simplifying x + 0.5625 = -1.751115716 Reorder the terms: 0.5625 + x = -1.751115716 Solving 0.5625 + x = -1.751115716 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 = -1.751115716 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = -1.751115716 + -0.5625 x = -1.751115716 + -0.5625 Combine like terms: -1.751115716 + -0.5625 = -2.313615716 x = -2.313615716 Simplifying x = -2.313615716

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.188615716, -2.313615716}

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