-70x-x^2+105=0

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Solution for -70x-x^2+105=0 equation:


Simplifying
-70x + -1x2 + 105 = 0

Reorder the terms:
105 + -70x + -1x2 = 0

Solving
105 + -70x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-105 + 70x + x2 = 0

Move the constant term to the right:

Add '105' to each side of the equation.
-105 + 70x + 105 + x2 = 0 + 105

Reorder the terms:
-105 + 105 + 70x + x2 = 0 + 105

Combine like terms: -105 + 105 = 0
0 + 70x + x2 = 0 + 105
70x + x2 = 0 + 105

Combine like terms: 0 + 105 = 105
70x + x2 = 105

The x term is 70x.  Take half its coefficient (35).
Square it (1225) and add it to both sides.

Add '1225' to each side of the equation.
70x + 1225 + x2 = 105 + 1225

Reorder the terms:
1225 + 70x + x2 = 105 + 1225

Combine like terms: 105 + 1225 = 1330
1225 + 70x + x2 = 1330

Factor a perfect square on the left side:
(x + 35)(x + 35) = 1330

Calculate the square root of the right side: 36.469165058

Break this problem into two subproblems by setting 
(x + 35) equal to 36.469165058 and -36.469165058.

Subproblem 1

x + 35 = 36.469165058 Simplifying x + 35 = 36.469165058 Reorder the terms: 35 + x = 36.469165058 Solving 35 + x = 36.469165058 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + x = 36.469165058 + -35 Combine like terms: 35 + -35 = 0 0 + x = 36.469165058 + -35 x = 36.469165058 + -35 Combine like terms: 36.469165058 + -35 = 1.469165058 x = 1.469165058 Simplifying x = 1.469165058

Subproblem 2

x + 35 = -36.469165058 Simplifying x + 35 = -36.469165058 Reorder the terms: 35 + x = -36.469165058 Solving 35 + x = -36.469165058 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + x = -36.469165058 + -35 Combine like terms: 35 + -35 = 0 0 + x = -36.469165058 + -35 x = -36.469165058 + -35 Combine like terms: -36.469165058 + -35 = -71.469165058 x = -71.469165058 Simplifying x = -71.469165058

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.469165058, -71.469165058}

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