-100x^2+70x+100=0

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Solution for -100x^2+70x+100=0 equation: 


Simplifying
-100x2 + 70x + 100 = 0

Reorder the terms:
100 + 70x + -100x2 = 0

Solving
100 + 70x + -100x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(10 + 7x + -10x2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(10 + 7x + -10x2)' equal to zero and attempt to solve:

Simplifying
10 + 7x + -10x2 = 0

Solving
10 + 7x + -10x2 = 0

Begin completing the square.  Divide all terms by
-10 the coefficient of the squared term: 

Divide each side by '-10'.
-1 + -0.7x + x2 = 0.0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -0.7x + 1 + x2 = 0.0 + 1

Reorder the terms:
-1 + 1 + -0.7x + x2 = 0.0 + 1

Combine like terms: -1 + 1 = 0
0 + -0.7x + x2 = 0.0 + 1
-0.7x + x2 = 0.0 + 1

Combine like terms: 0.0 + 1 = 1
-0.7x + x2 = 1

The x term is -0.7x.  Take half its coefficient (-0.35).
Square it (0.1225) and add it to both sides.

Add '0.1225' to each side of the equation.
-0.7x + 0.1225 + x2 = 1 + 0.1225

Reorder the terms:
0.1225 + -0.7x + x2 = 1 + 0.1225

Combine like terms: 1 + 0.1225 = 1.1225
0.1225 + -0.7x + x2 = 1.1225

Factor a perfect square on the left side:
(x + -0.35)(x + -0.35) = 1.1225

Calculate the square root of the right side: 1.059481005

Break this problem into two subproblems by setting 
(x + -0.35) equal to 1.059481005 and -1.059481005.


Subproblem 1
x + -0.35 = 1.059481005

Simplifying
x + -0.35 = 1.059481005

Reorder the terms:
-0.35 + x = 1.059481005

Solving
-0.35 + x = 1.059481005

Solving for variable 'x'.

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

Add '0.35' to each side of the equation.
-0.35 + 0.35 + x = 1.059481005 + 0.35

Combine like terms: -0.35 + 0.35 = 0.00
0.00 + x = 1.059481005 + 0.35
x = 1.059481005 + 0.35

Combine like terms: 1.059481005 + 0.35 = 1.409481005
x = 1.409481005

Simplifying
x = 1.409481005


Subproblem 2
x + -0.35 = -1.059481005

Simplifying
x + -0.35 = -1.059481005

Reorder the terms:
-0.35 + x = -1.059481005

Solving
-0.35 + x = -1.059481005

Solving for variable 'x'.

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

Add '0.35' to each side of the equation.
-0.35 + 0.35 + x = -1.059481005 + 0.35

Combine like terms: -0.35 + 0.35 = 0.00
0.00 + x = -1.059481005 + 0.35
x = -1.059481005 + 0.35

Combine like terms: -1.059481005 + 0.35 = -0.709481005
x = -0.709481005

Simplifying
x = -0.709481005


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.409481005, -0.709481005}
Solution
x = {1.409481005, -0.709481005}

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