9a^2=-8a+10

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Solution for 9a^2=-8a+10 equation:


Simplifying
9a2 = -8a + 10

Reorder the terms:
9a2 = 10 + -8a

Solving
9a2 = 10 + -8a

Solving for variable 'a'.

Reorder the terms:
-10 + 8a + 9a2 = 10 + -8a + -10 + 8a

Reorder the terms:
-10 + 8a + 9a2 = 10 + -10 + -8a + 8a

Combine like terms: 10 + -10 = 0
-10 + 8a + 9a2 = 0 + -8a + 8a
-10 + 8a + 9a2 = -8a + 8a

Combine like terms: -8a + 8a = 0
-10 + 8a + 9a2 = 0

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

Divide each side by '9'.
-1.111111111 + 0.8888888889a + a2 = 0

Move the constant term to the right:

Add '1.111111111' to each side of the equation.
-1.111111111 + 0.8888888889a + 1.111111111 + a2 = 0 + 1.111111111

Reorder the terms:
-1.111111111 + 1.111111111 + 0.8888888889a + a2 = 0 + 1.111111111

Combine like terms: -1.111111111 + 1.111111111 = 0.000000000
0.000000000 + 0.8888888889a + a2 = 0 + 1.111111111
0.8888888889a + a2 = 0 + 1.111111111

Combine like terms: 0 + 1.111111111 = 1.111111111
0.8888888889a + a2 = 1.111111111

The a term is 0.8888888889a.  Take half its coefficient (0.4444444445).
Square it (0.1975308642) and add it to both sides.

Add '0.1975308642' to each side of the equation.
0.8888888889a + 0.1975308642 + a2 = 1.111111111 + 0.1975308642

Reorder the terms:
0.1975308642 + 0.8888888889a + a2 = 1.111111111 + 0.1975308642

Combine like terms: 1.111111111 + 0.1975308642 = 1.3086419752
0.1975308642 + 0.8888888889a + a2 = 1.3086419752

Factor a perfect square on the left side:
(a + 0.4444444445)(a + 0.4444444445) = 1.3086419752

Calculate the square root of the right side: 1.143958905

Break this problem into two subproblems by setting 
(a + 0.4444444445) equal to 1.143958905 and -1.143958905.

Subproblem 1

a + 0.4444444445 = 1.143958905 Simplifying a + 0.4444444445 = 1.143958905 Reorder the terms: 0.4444444445 + a = 1.143958905 Solving 0.4444444445 + a = 1.143958905 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + a = 1.143958905 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + a = 1.143958905 + -0.4444444445 a = 1.143958905 + -0.4444444445 Combine like terms: 1.143958905 + -0.4444444445 = 0.6995144605 a = 0.6995144605 Simplifying a = 0.6995144605

Subproblem 2

a + 0.4444444445 = -1.143958905 Simplifying a + 0.4444444445 = -1.143958905 Reorder the terms: 0.4444444445 + a = -1.143958905 Solving 0.4444444445 + a = -1.143958905 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + a = -1.143958905 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + a = -1.143958905 + -0.4444444445 a = -1.143958905 + -0.4444444445 Combine like terms: -1.143958905 + -0.4444444445 = -1.5884033495 a = -1.5884033495 Simplifying a = -1.5884033495

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.6995144605, -1.5884033495}

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