7x+32=x^2+4

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Solution for 7x+32=x^2+4 equation:


Simplifying
7x + 32 = x2 + 4

Reorder the terms:
32 + 7x = x2 + 4

Reorder the terms:
32 + 7x = 4 + x2

Solving
32 + 7x = 4 + x2

Solving for variable 'x'.

Reorder the terms:
32 + -4 + 7x + -1x2 = 4 + x2 + -4 + -1x2

Combine like terms: 32 + -4 = 28
28 + 7x + -1x2 = 4 + x2 + -4 + -1x2

Reorder the terms:
28 + 7x + -1x2 = 4 + -4 + x2 + -1x2

Combine like terms: 4 + -4 = 0
28 + 7x + -1x2 = 0 + x2 + -1x2
28 + 7x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
28 + 7x + -1x2 = 0

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

Divide each side by '-1'.
-28 + -7x + x2 = 0

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + -7x + 28 + x2 = 0 + 28

Reorder the terms:
-28 + 28 + -7x + x2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + -7x + x2 = 0 + 28
-7x + x2 = 0 + 28

Combine like terms: 0 + 28 = 28
-7x + x2 = 28

The x term is -7x.  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.
-7x + 12.25 + x2 = 28 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 28 + 12.25

Combine like terms: 28 + 12.25 = 40.25
12.25 + -7x + x2 = 40.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 40.25

Calculate the square root of the right side: 6.34428877

Break this problem into two subproblems by setting 
(x + -3.5) equal to 6.34428877 and -6.34428877.

Subproblem 1

x + -3.5 = 6.34428877 Simplifying x + -3.5 = 6.34428877 Reorder the terms: -3.5 + x = 6.34428877 Solving -3.5 + x = 6.34428877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 6.34428877 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 6.34428877 + 3.5 x = 6.34428877 + 3.5 Combine like terms: 6.34428877 + 3.5 = 9.84428877 x = 9.84428877 Simplifying x = 9.84428877

Subproblem 2

x + -3.5 = -6.34428877 Simplifying x + -3.5 = -6.34428877 Reorder the terms: -3.5 + x = -6.34428877 Solving -3.5 + x = -6.34428877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -6.34428877 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -6.34428877 + 3.5 x = -6.34428877 + 3.5 Combine like terms: -6.34428877 + 3.5 = -2.84428877 x = -2.84428877 Simplifying x = -2.84428877

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.84428877, -2.84428877}

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