0.05x^2+0.7x-50=0

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Solution for 0.05x^2+0.7x-50=0 equation:


Simplifying
0.05x2 + 0.7x + -50 = 0

Reorder the terms:
-50 + 0.7x + 0.05x2 = 0

Solving
-50 + 0.7x + 0.05x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.05'.
-1000 + 14x + x2 = 0

Move the constant term to the right:

Add '1000' to each side of the equation.
-1000 + 14x + 1000 + x2 = 0 + 1000

Reorder the terms:
-1000 + 1000 + 14x + x2 = 0 + 1000

Combine like terms: -1000 + 1000 = 0
0 + 14x + x2 = 0 + 1000
14x + x2 = 0 + 1000

Combine like terms: 0 + 1000 = 1000
14x + x2 = 1000

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = 1000 + 49

Reorder the terms:
49 + 14x + x2 = 1000 + 49

Combine like terms: 1000 + 49 = 1049
49 + 14x + x2 = 1049

Factor a perfect square on the left side:
(x + 7)(x + 7) = 1049

Calculate the square root of the right side: 32.388269481

Break this problem into two subproblems by setting 
(x + 7) equal to 32.388269481 and -32.388269481.

Subproblem 1

x + 7 = 32.388269481 Simplifying x + 7 = 32.388269481 Reorder the terms: 7 + x = 32.388269481 Solving 7 + x = 32.388269481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 32.388269481 + -7 Combine like terms: 7 + -7 = 0 0 + x = 32.388269481 + -7 x = 32.388269481 + -7 Combine like terms: 32.388269481 + -7 = 25.388269481 x = 25.388269481 Simplifying x = 25.388269481

Subproblem 2

x + 7 = -32.388269481 Simplifying x + 7 = -32.388269481 Reorder the terms: 7 + x = -32.388269481 Solving 7 + x = -32.388269481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -32.388269481 + -7 Combine like terms: 7 + -7 = 0 0 + x = -32.388269481 + -7 x = -32.388269481 + -7 Combine like terms: -32.388269481 + -7 = -39.388269481 x = -39.388269481 Simplifying x = -39.388269481

Solution

The solution to the problem is based on the solutions from the subproblems. x = {25.388269481, -39.388269481}

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