x^2+14x-24.5=0

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Solution for x^2+14x-24.5=0 equation: 


Simplifying
x2 + 14x + -24.5 = 0

Reorder the terms:
-24.5 + 14x + x2 = 0

Solving
-24.5 + 14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '24.5' to each side of the equation.
-24.5 + 14x + 24.5 + x2 = 0 + 24.5

Reorder the terms:
-24.5 + 24.5 + 14x + x2 = 0 + 24.5

Combine like terms: -24.5 + 24.5 = 0.0
0.0 + 14x + x2 = 0 + 24.5
14x + x2 = 0 + 24.5

Combine like terms: 0 + 24.5 = 24.5
14x + x2 = 24.5

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 = 24.5 + 49

Reorder the terms:
49 + 14x + x2 = 24.5 + 49

Combine like terms: 24.5 + 49 = 73.5
49 + 14x + x2 = 73.5

Factor a perfect square on the left side:
(x + 7)(x + 7) = 73.5

Calculate the square root of the right side: 8.5732141

Break this problem into two subproblems by setting 
(x + 7) equal to 8.5732141 and -8.5732141.


Subproblem 1
x + 7 = 8.5732141

Simplifying
x + 7 = 8.5732141

Reorder the terms:
7 + x = 8.5732141

Solving
7 + x = 8.5732141

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 = 8.5732141 + -7

Combine like terms: 7 + -7 = 0
0 + x = 8.5732141 + -7
x = 8.5732141 + -7

Combine like terms: 8.5732141 + -7 = 1.5732141
x = 1.5732141

Simplifying
x = 1.5732141


Subproblem 2
x + 7 = -8.5732141

Simplifying
x + 7 = -8.5732141

Reorder the terms:
7 + x = -8.5732141

Solving
7 + x = -8.5732141

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 = -8.5732141 + -7

Combine like terms: 7 + -7 = 0
0 + x = -8.5732141 + -7
x = -8.5732141 + -7

Combine like terms: -8.5732141 + -7 = -15.5732141
x = -15.5732141

Simplifying
x = -15.5732141


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.5732141, -15.5732141}

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