0.1x^2-0.7x+1=0

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Solution for 0.1x^2-0.7x+1=0 equation:


Simplifying
0.1x2 + -0.7x + 1 = 0

Reorder the terms:
1 + -0.7x + 0.1x2 = 0

Solving
1 + -0.7x + 0.1x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.1'.
10 + -7x + x2 = 0

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -7x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + -7x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -7x + x2 = 0 + -10
-7x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
-7x + x2 = -10

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 = -10 + 12.25

Reorder the terms:
12.25 + -7x + x2 = -10 + 12.25

Combine like terms: -10 + 12.25 = 2.25
12.25 + -7x + x2 = 2.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 2.25

Calculate the square root of the right side: 1.5

Break this problem into two subproblems by setting 
(x + -3.5) equal to 1.5 and -1.5.

Subproblem 1

x + -3.5 = 1.5 Simplifying x + -3.5 = 1.5 Reorder the terms: -3.5 + x = 1.5 Solving -3.5 + x = 1.5 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 = 1.5 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 1.5 + 3.5 x = 1.5 + 3.5 Combine like terms: 1.5 + 3.5 = 5 x = 5 Simplifying x = 5

Subproblem 2

x + -3.5 = -1.5 Simplifying x + -3.5 = -1.5 Reorder the terms: -3.5 + x = -1.5 Solving -3.5 + x = -1.5 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 = -1.5 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -1.5 + 3.5 x = -1.5 + 3.5 Combine like terms: -1.5 + 3.5 = 2 x = 2 Simplifying x = 2

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5, 2}

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