x^2+9x+1=7

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Solution for x^2+9x+1=7 equation:


Simplifying
x2 + 9x + 1 = 7

Reorder the terms:
1 + 9x + x2 = 7

Solving
1 + 9x + x2 = 7

Solving for variable 'x'.

Reorder the terms:
1 + -7 + 9x + x2 = 7 + -7

Combine like terms: 1 + -7 = -6
-6 + 9x + x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-6 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 9x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + 9x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 9x + x2 = 0 + 6
9x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
9x + x2 = 6

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = 6 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 6 + 20.25

Combine like terms: 6 + 20.25 = 26.25
20.25 + 9x + x2 = 26.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 26.25

Calculate the square root of the right side: 5.123475383

Break this problem into two subproblems by setting 
(x + 4.5) equal to 5.123475383 and -5.123475383.

Subproblem 1

x + 4.5 = 5.123475383 Simplifying x + 4.5 = 5.123475383 Reorder the terms: 4.5 + x = 5.123475383 Solving 4.5 + x = 5.123475383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 5.123475383 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 5.123475383 + -4.5 x = 5.123475383 + -4.5 Combine like terms: 5.123475383 + -4.5 = 0.623475383 x = 0.623475383 Simplifying x = 0.623475383

Subproblem 2

x + 4.5 = -5.123475383 Simplifying x + 4.5 = -5.123475383 Reorder the terms: 4.5 + x = -5.123475383 Solving 4.5 + x = -5.123475383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -5.123475383 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -5.123475383 + -4.5 x = -5.123475383 + -4.5 Combine like terms: -5.123475383 + -4.5 = -9.623475383 x = -9.623475383 Simplifying x = -9.623475383

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.623475383, -9.623475383}

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