a^2-7a=-7

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


Simplifying
a2 + -7a = -7

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

Solving
-7a + a2 = -7

Solving for variable 'a'.

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

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

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -7a + -7 + a2 = 0 + -7

Reorder the terms:
7 + -7 + -7a + a2 = 0 + -7

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

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

The a term is -7a.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7a + 12.25 + a2 = -7 + 12.25

Reorder the terms:
12.25 + -7a + a2 = -7 + 12.25

Combine like terms: -7 + 12.25 = 5.25
12.25 + -7a + a2 = 5.25

Factor a perfect square on the left side:
(a + -3.5)(a + -3.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(a + -3.5) equal to 2.291287847 and -2.291287847.

Subproblem 1

a + -3.5 = 2.291287847 Simplifying a + -3.5 = 2.291287847 Reorder the terms: -3.5 + a = 2.291287847 Solving -3.5 + a = 2.291287847 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + a = 2.291287847 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + a = 2.291287847 + 3.5 a = 2.291287847 + 3.5 Combine like terms: 2.291287847 + 3.5 = 5.791287847 a = 5.791287847 Simplifying a = 5.791287847

Subproblem 2

a + -3.5 = -2.291287847 Simplifying a + -3.5 = -2.291287847 Reorder the terms: -3.5 + a = -2.291287847 Solving -3.5 + a = -2.291287847 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + a = -2.291287847 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + a = -2.291287847 + 3.5 a = -2.291287847 + 3.5 Combine like terms: -2.291287847 + 3.5 = 1.208712153 a = 1.208712153 Simplifying a = 1.208712153

Solution

The solution to the problem is based on the solutions from the subproblems. a = {5.791287847, 1.208712153}

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