x^2+10x-42=0

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Solution for x^2+10x-42=0 equation:


Simplifying
x2 + 10x + -42 = 0

Reorder the terms:
-42 + 10x + x2 = 0

Solving
-42 + 10x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '42' to each side of the equation.
-42 + 10x + 42 + x2 = 0 + 42

Reorder the terms:
-42 + 42 + 10x + x2 = 0 + 42

Combine like terms: -42 + 42 = 0
0 + 10x + x2 = 0 + 42
10x + x2 = 0 + 42

Combine like terms: 0 + 42 = 42
10x + x2 = 42

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 42 + 25

Reorder the terms:
25 + 10x + x2 = 42 + 25

Combine like terms: 42 + 25 = 67
25 + 10x + x2 = 67

Factor a perfect square on the left side:
(x + 5)(x + 5) = 67

Calculate the square root of the right side: 8.185352772

Break this problem into two subproblems by setting 
(x + 5) equal to 8.185352772 and -8.185352772.

Subproblem 1

x + 5 = 8.185352772 Simplifying x + 5 = 8.185352772 Reorder the terms: 5 + x = 8.185352772 Solving 5 + x = 8.185352772 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 8.185352772 + -5 Combine like terms: 5 + -5 = 0 0 + x = 8.185352772 + -5 x = 8.185352772 + -5 Combine like terms: 8.185352772 + -5 = 3.185352772 x = 3.185352772 Simplifying x = 3.185352772

Subproblem 2

x + 5 = -8.185352772 Simplifying x + 5 = -8.185352772 Reorder the terms: 5 + x = -8.185352772 Solving 5 + x = -8.185352772 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -8.185352772 + -5 Combine like terms: 5 + -5 = 0 0 + x = -8.185352772 + -5 x = -8.185352772 + -5 Combine like terms: -8.185352772 + -5 = -13.185352772 x = -13.185352772 Simplifying x = -13.185352772

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.185352772, -13.185352772}

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