24=14x+x^2

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Solution for 24=14x+x^2 equation:


Simplifying
24 = 14x + x2

Solving
24 = 14x + x2

Solving for variable 'x'.

Reorder the terms:
24 + -14x + -1x2 = 14x + -14x + x2 + -1x2

Combine like terms: 14x + -14x = 0
24 + -14x + -1x2 = 0 + x2 + -1x2
24 + -14x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
24 + -14x + -1x2 = 0

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

Divide each side by '-1'.
-24 + 14x + x2 = 0

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + 14x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + 14x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + 14x + x2 = 0 + 24
14x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
14x + x2 = 24

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = 24 + 49

Reorder the terms:
49 + 14x + x2 = 24 + 49

Combine like terms: 24 + 49 = 73
49 + 14x + x2 = 73

Factor a perfect square on the left side:
(x + 7)(x + 7) = 73

Calculate the square root of the right side: 8.544003745

Break this problem into two subproblems by setting 
(x + 7) equal to 8.544003745 and -8.544003745.

Subproblem 1

x + 7 = 8.544003745 Simplifying x + 7 = 8.544003745 Reorder the terms: 7 + x = 8.544003745 Solving 7 + x = 8.544003745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 8.544003745 + -7 Combine like terms: 7 + -7 = 0 0 + x = 8.544003745 + -7 x = 8.544003745 + -7 Combine like terms: 8.544003745 + -7 = 1.544003745 x = 1.544003745 Simplifying x = 1.544003745

Subproblem 2

x + 7 = -8.544003745 Simplifying x + 7 = -8.544003745 Reorder the terms: 7 + x = -8.544003745 Solving 7 + x = -8.544003745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -8.544003745 + -7 Combine like terms: 7 + -7 = 0 0 + x = -8.544003745 + -7 x = -8.544003745 + -7 Combine like terms: -8.544003745 + -7 = -15.544003745 x = -15.544003745 Simplifying x = -15.544003745

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.544003745, -15.544003745}

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