4x+17=x^2+9

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Solution for 4x+17=x^2+9 equation:


Simplifying
4x + 17 = x2 + 9

Reorder the terms:
17 + 4x = x2 + 9

Reorder the terms:
17 + 4x = 9 + x2

Solving
17 + 4x = 9 + x2

Solving for variable 'x'.

Reorder the terms:
17 + -9 + 4x + -1x2 = 9 + x2 + -9 + -1x2

Combine like terms: 17 + -9 = 8
8 + 4x + -1x2 = 9 + x2 + -9 + -1x2

Reorder the terms:
8 + 4x + -1x2 = 9 + -9 + x2 + -1x2

Combine like terms: 9 + -9 = 0
8 + 4x + -1x2 = 0 + x2 + -1x2
8 + 4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
8 + 4x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-8 + -4x + x2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -4x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + -4x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -4x + x2 = 0 + 8
-4x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
-4x + x2 = 8

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 8 + 4

Reorder the terms:
4 + -4x + x2 = 8 + 4

Combine like terms: 8 + 4 = 12
4 + -4x + x2 = 12

Factor a perfect square on the left side:
(x + -2)(x + -2) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(x + -2) equal to 3.464101615 and -3.464101615.

Subproblem 1

x + -2 = 3.464101615 Simplifying x + -2 = 3.464101615 Reorder the terms: -2 + x = 3.464101615 Solving -2 + x = 3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 3.464101615 + 2 Combine like terms: -2 + 2 = 0 0 + x = 3.464101615 + 2 x = 3.464101615 + 2 Combine like terms: 3.464101615 + 2 = 5.464101615 x = 5.464101615 Simplifying x = 5.464101615

Subproblem 2

x + -2 = -3.464101615 Simplifying x + -2 = -3.464101615 Reorder the terms: -2 + x = -3.464101615 Solving -2 + x = -3.464101615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -3.464101615 + 2 Combine like terms: -2 + 2 = 0 0 + x = -3.464101615 + 2 x = -3.464101615 + 2 Combine like terms: -3.464101615 + 2 = -1.464101615 x = -1.464101615 Simplifying x = -1.464101615

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.464101615, -1.464101615}

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