0.7x^2-7x+11.2=0

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Solution for 0.7x^2-7x+11.2=0 equation:


Simplifying
0.7x2 + -7x + 11.2 = 0

Reorder the terms:
11.2 + -7x + 0.7x2 = 0

Solving
11.2 + -7x + 0.7x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.7'.
16 + -10x + x2 = 0

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + -10x + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + -10x + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -10x + x2 = 0 + -16
-10x + x2 = 0 + -16

Combine like terms: 0 + -16 = -16
-10x + x2 = -16

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = -16 + 25

Reorder the terms:
25 + -10x + x2 = -16 + 25

Combine like terms: -16 + 25 = 9
25 + -10x + x2 = 9

Factor a perfect square on the left side:
(x + -5)(x + -5) = 9

Calculate the square root of the right side: 3

Break this problem into two subproblems by setting 
(x + -5) equal to 3 and -3.

Subproblem 1

x + -5 = 3 Simplifying x + -5 = 3 Reorder the terms: -5 + x = 3 Solving -5 + x = 3 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 3 + 5 Combine like terms: -5 + 5 = 0 0 + x = 3 + 5 x = 3 + 5 Combine like terms: 3 + 5 = 8 x = 8 Simplifying x = 8

Subproblem 2

x + -5 = -3 Simplifying x + -5 = -3 Reorder the terms: -5 + x = -3 Solving -5 + x = -3 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -3 + 5 Combine like terms: -5 + 5 = 0 0 + x = -3 + 5 x = -3 + 5 Combine like terms: -3 + 5 = 2 x = 2 Simplifying x = 2

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8, 2}

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