x^2-8.4x-151.36=0

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Solution for x^2-8.4x-151.36=0 equation: 


Simplifying
x2 + -8.4x + -151.36 = 0

Reorder the terms:
-151.36 + -8.4x + x2 = 0

Solving
-151.36 + -8.4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '151.36' to each side of the equation.
-151.36 + -8.4x + 151.36 + x2 = 0 + 151.36

Reorder the terms:
-151.36 + 151.36 + -8.4x + x2 = 0 + 151.36

Combine like terms: -151.36 + 151.36 = 0.00
0.00 + -8.4x + x2 = 0 + 151.36
-8.4x + x2 = 0 + 151.36

Combine like terms: 0 + 151.36 = 151.36
-8.4x + x2 = 151.36

The x term is -8.4x.  Take half its coefficient (-4.2).
Square it (17.64) and add it to both sides.

Add '17.64' to each side of the equation.
-8.4x + 17.64 + x2 = 151.36 + 17.64

Reorder the terms:
17.64 + -8.4x + x2 = 151.36 + 17.64

Combine like terms: 151.36 + 17.64 = 169
17.64 + -8.4x + x2 = 169

Factor a perfect square on the left side:
(x + -4.2)(x + -4.2) = 169

Calculate the square root of the right side: 13

Break this problem into two subproblems by setting 
(x + -4.2) equal to 13 and -13.


Subproblem 1
x + -4.2 = 13

Simplifying
x + -4.2 = 13

Reorder the terms:
-4.2 + x = 13

Solving
-4.2 + x = 13

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4.2' to each side of the equation.
-4.2 + 4.2 + x = 13 + 4.2

Combine like terms: -4.2 + 4.2 = 0.0
0.0 + x = 13 + 4.2
x = 13 + 4.2

Combine like terms: 13 + 4.2 = 17.2
x = 17.2

Simplifying
x = 17.2


Subproblem 2
x + -4.2 = -13

Simplifying
x + -4.2 = -13

Reorder the terms:
-4.2 + x = -13

Solving
-4.2 + x = -13

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4.2' to each side of the equation.
-4.2 + 4.2 + x = -13 + 4.2

Combine like terms: -4.2 + 4.2 = 0.0
0.0 + x = -13 + 4.2
x = -13 + 4.2

Combine like terms: -13 + 4.2 = -8.8
x = -8.8

Simplifying
x = -8.8


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.2, -8.8}

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