x^2+1x-35=0

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Solution for x^2+1x-35=0 equation:


Simplifying
x2 + 1x + -35 = 0

Reorder the terms:
-35 + 1x + x2 = 0

Solving
-35 + 1x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '35' to each side of the equation.
-35 + 1x + 35 + x2 = 0 + 35

Reorder the terms:
-35 + 35 + 1x + x2 = 0 + 35

Combine like terms: -35 + 35 = 0
0 + 1x + x2 = 0 + 35
1x + x2 = 0 + 35

Combine like terms: 0 + 35 = 35
1x + x2 = 35

The x term is 1x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 35 + 0.25

Reorder the terms:
0.25 + x + x2 = 35 + 0.25

Combine like terms: 35 + 0.25 = 35.25
0.25 + x + x2 = 35.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 35.25

Calculate the square root of the right side: 5.937171044

Break this problem into two subproblems by setting 
(x + 0.5) equal to 5.937171044 and -5.937171044.

Subproblem 1

x + 0.5 = 5.937171044 Simplifying x + 0.5 = 5.937171044 Reorder the terms: 0.5 + x = 5.937171044 Solving 0.5 + x = 5.937171044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 5.937171044 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 5.937171044 + -0.5 x = 5.937171044 + -0.5 Combine like terms: 5.937171044 + -0.5 = 5.437171044 x = 5.437171044 Simplifying x = 5.437171044

Subproblem 2

x + 0.5 = -5.937171044 Simplifying x + 0.5 = -5.937171044 Reorder the terms: 0.5 + x = -5.937171044 Solving 0.5 + x = -5.937171044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -5.937171044 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -5.937171044 + -0.5 x = -5.937171044 + -0.5 Combine like terms: -5.937171044 + -0.5 = -6.437171044 x = -6.437171044 Simplifying x = -6.437171044

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.437171044, -6.437171044}

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