10a^2-7a=1

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Solution for 10a^2-7a=1 equation:


Simplifying
10a2 + -7a = 1

Reorder the terms:
-7a + 10a2 = 1

Solving
-7a + 10a2 = 1

Solving for variable 'a'.

Reorder the terms:
-1 + -7a + 10a2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + -7a + 10a2 = 0

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

Divide each side by '10'.
-0.1 + -0.7a + a2 = 0

Move the constant term to the right:

Add '0.1' to each side of the equation.
-0.1 + -0.7a + 0.1 + a2 = 0 + 0.1

Reorder the terms:
-0.1 + 0.1 + -0.7a + a2 = 0 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + -0.7a + a2 = 0 + 0.1
-0.7a + a2 = 0 + 0.1

Combine like terms: 0 + 0.1 = 0.1
-0.7a + a2 = 0.1

The a term is -0.7a.  Take half its coefficient (-0.35).
Square it (0.1225) and add it to both sides.

Add '0.1225' to each side of the equation.
-0.7a + 0.1225 + a2 = 0.1 + 0.1225

Reorder the terms:
0.1225 + -0.7a + a2 = 0.1 + 0.1225

Combine like terms: 0.1 + 0.1225 = 0.2225
0.1225 + -0.7a + a2 = 0.2225

Factor a perfect square on the left side:
(a + -0.35)(a + -0.35) = 0.2225

Calculate the square root of the right side: 0.471699057

Break this problem into two subproblems by setting 
(a + -0.35) equal to 0.471699057 and -0.471699057.

Subproblem 1

a + -0.35 = 0.471699057 Simplifying a + -0.35 = 0.471699057 Reorder the terms: -0.35 + a = 0.471699057 Solving -0.35 + a = 0.471699057 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + a = 0.471699057 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + a = 0.471699057 + 0.35 a = 0.471699057 + 0.35 Combine like terms: 0.471699057 + 0.35 = 0.821699057 a = 0.821699057 Simplifying a = 0.821699057

Subproblem 2

a + -0.35 = -0.471699057 Simplifying a + -0.35 = -0.471699057 Reorder the terms: -0.35 + a = -0.471699057 Solving -0.35 + a = -0.471699057 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + a = -0.471699057 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + a = -0.471699057 + 0.35 a = -0.471699057 + 0.35 Combine like terms: -0.471699057 + 0.35 = -0.121699057 a = -0.121699057 Simplifying a = -0.121699057

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.821699057, -0.121699057}

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