x^2+35x=42

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Solution for x^2+35x=42 equation:


Simplifying
x2 + 35x = 42

Reorder the terms:
35x + x2 = 42

Solving
35x + x2 = 42

Solving for variable 'x'.

Reorder the terms:
-42 + 35x + x2 = 42 + -42

Combine like terms: 42 + -42 = 0
-42 + 35x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '42' to each side of the equation.
-42 + 35x + 42 + x2 = 0 + 42

Reorder the terms:
-42 + 42 + 35x + x2 = 0 + 42

Combine like terms: -42 + 42 = 0
0 + 35x + x2 = 0 + 42
35x + x2 = 0 + 42

Combine like terms: 0 + 42 = 42
35x + x2 = 42

The x term is 35x.  Take half its coefficient (17.5).
Square it (306.25) and add it to both sides.

Add '306.25' to each side of the equation.
35x + 306.25 + x2 = 42 + 306.25

Reorder the terms:
306.25 + 35x + x2 = 42 + 306.25

Combine like terms: 42 + 306.25 = 348.25
306.25 + 35x + x2 = 348.25

Factor a perfect square on the left side:
(x + 17.5)(x + 17.5) = 348.25

Calculate the square root of the right side: 18.661457607

Break this problem into two subproblems by setting 
(x + 17.5) equal to 18.661457607 and -18.661457607.

Subproblem 1

x + 17.5 = 18.661457607 Simplifying x + 17.5 = 18.661457607 Reorder the terms: 17.5 + x = 18.661457607 Solving 17.5 + x = 18.661457607 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = 18.661457607 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = 18.661457607 + -17.5 x = 18.661457607 + -17.5 Combine like terms: 18.661457607 + -17.5 = 1.161457607 x = 1.161457607 Simplifying x = 1.161457607

Subproblem 2

x + 17.5 = -18.661457607 Simplifying x + 17.5 = -18.661457607 Reorder the terms: 17.5 + x = -18.661457607 Solving 17.5 + x = -18.661457607 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = -18.661457607 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = -18.661457607 + -17.5 x = -18.661457607 + -17.5 Combine like terms: -18.661457607 + -17.5 = -36.161457607 x = -36.161457607 Simplifying x = -36.161457607

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.161457607, -36.161457607}

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