x^2+8x-42=0

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Solution for x^2+8x-42=0 equation:


Simplifying
x2 + 8x + -42 = 0

Reorder the terms:
-42 + 8x + x2 = 0

Solving
-42 + 8x + 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 + 8x + 42 + x2 = 0 + 42

Reorder the terms:
-42 + 42 + 8x + x2 = 0 + 42

Combine like terms: -42 + 42 = 0
0 + 8x + x2 = 0 + 42
8x + x2 = 0 + 42

Combine like terms: 0 + 42 = 42
8x + x2 = 42

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 42 + 16

Reorder the terms:
16 + 8x + x2 = 42 + 16

Combine like terms: 42 + 16 = 58
16 + 8x + x2 = 58

Factor a perfect square on the left side:
(x + 4)(x + 4) = 58

Calculate the square root of the right side: 7.615773106

Break this problem into two subproblems by setting 
(x + 4) equal to 7.615773106 and -7.615773106.

Subproblem 1

x + 4 = 7.615773106 Simplifying x + 4 = 7.615773106 Reorder the terms: 4 + x = 7.615773106 Solving 4 + x = 7.615773106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 7.615773106 + -4 Combine like terms: 4 + -4 = 0 0 + x = 7.615773106 + -4 x = 7.615773106 + -4 Combine like terms: 7.615773106 + -4 = 3.615773106 x = 3.615773106 Simplifying x = 3.615773106

Subproblem 2

x + 4 = -7.615773106 Simplifying x + 4 = -7.615773106 Reorder the terms: 4 + x = -7.615773106 Solving 4 + x = -7.615773106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -7.615773106 + -4 Combine like terms: 4 + -4 = 0 0 + x = -7.615773106 + -4 x = -7.615773106 + -4 Combine like terms: -7.615773106 + -4 = -11.615773106 x = -11.615773106 Simplifying x = -11.615773106

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.615773106, -11.615773106}

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