7x=x^2-22

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Solution for 7x=x^2-22 equation:


Simplifying
7x = x2 + -22

Reorder the terms:
7x = -22 + x2

Solving
7x = -22 + x2

Solving for variable 'x'.

Reorder the terms:
22 + 7x + -1x2 = -22 + x2 + 22 + -1x2

Reorder the terms:
22 + 7x + -1x2 = -22 + 22 + x2 + -1x2

Combine like terms: -22 + 22 = 0
22 + 7x + -1x2 = 0 + x2 + -1x2
22 + 7x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
22 + 7x + -1x2 = 0

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

Divide each side by '-1'.
-22 + -7x + x2 = 0

Move the constant term to the right:

Add '22' to each side of the equation.
-22 + -7x + 22 + x2 = 0 + 22

Reorder the terms:
-22 + 22 + -7x + x2 = 0 + 22

Combine like terms: -22 + 22 = 0
0 + -7x + x2 = 0 + 22
-7x + x2 = 0 + 22

Combine like terms: 0 + 22 = 22
-7x + x2 = 22

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 = 22 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 22 + 12.25

Combine like terms: 22 + 12.25 = 34.25
12.25 + -7x + x2 = 34.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 34.25

Calculate the square root of the right side: 5.852349955

Break this problem into two subproblems by setting 
(x + -3.5) equal to 5.852349955 and -5.852349955.

Subproblem 1

x + -3.5 = 5.852349955 Simplifying x + -3.5 = 5.852349955 Reorder the terms: -3.5 + x = 5.852349955 Solving -3.5 + x = 5.852349955 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 = 5.852349955 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 5.852349955 + 3.5 x = 5.852349955 + 3.5 Combine like terms: 5.852349955 + 3.5 = 9.352349955 x = 9.352349955 Simplifying x = 9.352349955

Subproblem 2

x + -3.5 = -5.852349955 Simplifying x + -3.5 = -5.852349955 Reorder the terms: -3.5 + x = -5.852349955 Solving -3.5 + x = -5.852349955 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 = -5.852349955 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -5.852349955 + 3.5 x = -5.852349955 + 3.5 Combine like terms: -5.852349955 + 3.5 = -2.352349955 x = -2.352349955 Simplifying x = -2.352349955

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.352349955, -2.352349955}

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