x^2+14x-42=0

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Solution for x^2+14x-42=0 equation:


Simplifying
x2 + 14x + -42 = 0

Reorder the terms:
-42 + 14x + x2 = 0

Solving
-42 + 14x + 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 + 14x + 42 + x2 = 0 + 42

Reorder the terms:
-42 + 42 + 14x + x2 = 0 + 42

Combine like terms: -42 + 42 = 0
0 + 14x + x2 = 0 + 42
14x + x2 = 0 + 42

Combine like terms: 0 + 42 = 42
14x + x2 = 42

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 = 42 + 49

Reorder the terms:
49 + 14x + x2 = 42 + 49

Combine like terms: 42 + 49 = 91
49 + 14x + x2 = 91

Factor a perfect square on the left side:
(x + 7)(x + 7) = 91

Calculate the square root of the right side: 9.539392014

Break this problem into two subproblems by setting 
(x + 7) equal to 9.539392014 and -9.539392014.

Subproblem 1

x + 7 = 9.539392014 Simplifying x + 7 = 9.539392014 Reorder the terms: 7 + x = 9.539392014 Solving 7 + x = 9.539392014 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 = 9.539392014 + -7 Combine like terms: 7 + -7 = 0 0 + x = 9.539392014 + -7 x = 9.539392014 + -7 Combine like terms: 9.539392014 + -7 = 2.539392014 x = 2.539392014 Simplifying x = 2.539392014

Subproblem 2

x + 7 = -9.539392014 Simplifying x + 7 = -9.539392014 Reorder the terms: 7 + x = -9.539392014 Solving 7 + x = -9.539392014 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 = -9.539392014 + -7 Combine like terms: 7 + -7 = 0 0 + x = -9.539392014 + -7 x = -9.539392014 + -7 Combine like terms: -9.539392014 + -7 = -16.539392014 x = -16.539392014 Simplifying x = -16.539392014

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.539392014, -16.539392014}

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