105-28x=10x^2

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Solution for 105-28x=10x^2 equation:


Simplifying
105 + -28x = 10x2

Solving
105 + -28x = 10x2

Solving for variable 'x'.

Combine like terms: 10x2 + -10x2 = 0
105 + -28x + -10x2 = 0

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

Divide each side by '-10'.
-10.5 + 2.8x + x2 = 0

Move the constant term to the right:

Add '10.5' to each side of the equation.
-10.5 + 2.8x + 10.5 + x2 = 0 + 10.5

Reorder the terms:
-10.5 + 10.5 + 2.8x + x2 = 0 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + 2.8x + x2 = 0 + 10.5
2.8x + x2 = 0 + 10.5

Combine like terms: 0 + 10.5 = 10.5
2.8x + x2 = 10.5

The x term is 2.8x.  Take half its coefficient (1.4).
Square it (1.96) and add it to both sides.

Add '1.96' to each side of the equation.
2.8x + 1.96 + x2 = 10.5 + 1.96

Reorder the terms:
1.96 + 2.8x + x2 = 10.5 + 1.96

Combine like terms: 10.5 + 1.96 = 12.46
1.96 + 2.8x + x2 = 12.46

Factor a perfect square on the left side:
(x + 1.4)(x + 1.4) = 12.46

Calculate the square root of the right side: 3.529872519

Break this problem into two subproblems by setting 
(x + 1.4) equal to 3.529872519 and -3.529872519.

Subproblem 1

x + 1.4 = 3.529872519 Simplifying x + 1.4 = 3.529872519 Reorder the terms: 1.4 + x = 3.529872519 Solving 1.4 + x = 3.529872519 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + x = 3.529872519 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = 3.529872519 + -1.4 x = 3.529872519 + -1.4 Combine like terms: 3.529872519 + -1.4 = 2.129872519 x = 2.129872519 Simplifying x = 2.129872519

Subproblem 2

x + 1.4 = -3.529872519 Simplifying x + 1.4 = -3.529872519 Reorder the terms: 1.4 + x = -3.529872519 Solving 1.4 + x = -3.529872519 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + x = -3.529872519 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = -3.529872519 + -1.4 x = -3.529872519 + -1.4 Combine like terms: -3.529872519 + -1.4 = -4.929872519 x = -4.929872519 Simplifying x = -4.929872519

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.129872519, -4.929872519}

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