9x=8-5x^2

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Solution for 9x=8-5x^2 equation:


Simplifying
9x = 8 + -5x2

Solving
9x = 8 + -5x2

Solving for variable 'x'.

Reorder the terms:
-8 + 9x + 5x2 = 8 + -5x2 + -8 + 5x2

Reorder the terms:
-8 + 9x + 5x2 = 8 + -8 + -5x2 + 5x2

Combine like terms: 8 + -8 = 0
-8 + 9x + 5x2 = 0 + -5x2 + 5x2
-8 + 9x + 5x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
-8 + 9x + 5x2 = 0

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

Divide each side by '5'.
-1.6 + 1.8x + x2 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + 1.8x + 1.6 + x2 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + 1.8x + x2 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + 1.8x + x2 = 0 + 1.6
1.8x + x2 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
1.8x + x2 = 1.6

The x term is 1.8x.  Take half its coefficient (0.9).
Square it (0.81) and add it to both sides.

Add '0.81' to each side of the equation.
1.8x + 0.81 + x2 = 1.6 + 0.81

Reorder the terms:
0.81 + 1.8x + x2 = 1.6 + 0.81

Combine like terms: 1.6 + 0.81 = 2.41
0.81 + 1.8x + x2 = 2.41

Factor a perfect square on the left side:
(x + 0.9)(x + 0.9) = 2.41

Calculate the square root of the right side: 1.55241747

Break this problem into two subproblems by setting 
(x + 0.9) equal to 1.55241747 and -1.55241747.

Subproblem 1

x + 0.9 = 1.55241747 Simplifying x + 0.9 = 1.55241747 Reorder the terms: 0.9 + x = 1.55241747 Solving 0.9 + x = 1.55241747 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = 1.55241747 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 1.55241747 + -0.9 x = 1.55241747 + -0.9 Combine like terms: 1.55241747 + -0.9 = 0.65241747 x = 0.65241747 Simplifying x = 0.65241747

Subproblem 2

x + 0.9 = -1.55241747 Simplifying x + 0.9 = -1.55241747 Reorder the terms: 0.9 + x = -1.55241747 Solving 0.9 + x = -1.55241747 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = -1.55241747 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -1.55241747 + -0.9 x = -1.55241747 + -0.9 Combine like terms: -1.55241747 + -0.9 = -2.45241747 x = -2.45241747 Simplifying x = -2.45241747

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.65241747, -2.45241747}

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