(x^2+9x+3)+(7x-8)=

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Solution for (x^2+9x+3)+(7x-8)= equation:


Simplifying
(x2 + 9x + 3) + (7x + -8) = 0

Reorder the terms:
(3 + 9x + x2) + (7x + -8) = 0

Remove parenthesis around (3 + 9x + x2)
3 + 9x + x2 + (7x + -8) = 0

Reorder the terms:
3 + 9x + x2 + (-8 + 7x) = 0

Remove parenthesis around (-8 + 7x)
3 + 9x + x2 + -8 + 7x = 0

Reorder the terms:
3 + -8 + 9x + 7x + x2 = 0

Combine like terms: 3 + -8 = -5
-5 + 9x + 7x + x2 = 0

Combine like terms: 9x + 7x = 16x
-5 + 16x + x2 = 0

Solving
-5 + 16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 16x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + 16x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 16x + x2 = 0 + 5
16x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
16x + x2 = 5

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = 5 + 64

Reorder the terms:
64 + 16x + x2 = 5 + 64

Combine like terms: 5 + 64 = 69
64 + 16x + x2 = 69

Factor a perfect square on the left side:
(x + 8)(x + 8) = 69

Calculate the square root of the right side: 8.306623863

Break this problem into two subproblems by setting 
(x + 8) equal to 8.306623863 and -8.306623863.

Subproblem 1

x + 8 = 8.306623863 Simplifying x + 8 = 8.306623863 Reorder the terms: 8 + x = 8.306623863 Solving 8 + x = 8.306623863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 8.306623863 + -8 Combine like terms: 8 + -8 = 0 0 + x = 8.306623863 + -8 x = 8.306623863 + -8 Combine like terms: 8.306623863 + -8 = 0.306623863 x = 0.306623863 Simplifying x = 0.306623863

Subproblem 2

x + 8 = -8.306623863 Simplifying x + 8 = -8.306623863 Reorder the terms: 8 + x = -8.306623863 Solving 8 + x = -8.306623863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -8.306623863 + -8 Combine like terms: 8 + -8 = 0 0 + x = -8.306623863 + -8 x = -8.306623863 + -8 Combine like terms: -8.306623863 + -8 = -16.306623863 x = -16.306623863 Simplifying x = -16.306623863

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.306623863, -16.306623863}

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