8x^2+16x-42=1

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Solution for 8x^2+16x-42=1 equation:


Simplifying
8x2 + 16x + -42 = 1

Reorder the terms:
-42 + 16x + 8x2 = 1

Solving
-42 + 16x + 8x2 = 1

Solving for variable 'x'.

Reorder the terms:
-42 + -1 + 16x + 8x2 = 1 + -1

Combine like terms: -42 + -1 = -43
-43 + 16x + 8x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-43 + 16x + 8x2 = 0

Begin completing the square.  Divide all terms by
8 the coefficient of the squared term: 

Divide each side by '8'.
-5.375 + 2x + x2 = 0

Move the constant term to the right:

Add '5.375' to each side of the equation.
-5.375 + 2x + 5.375 + x2 = 0 + 5.375

Reorder the terms:
-5.375 + 5.375 + 2x + x2 = 0 + 5.375

Combine like terms: -5.375 + 5.375 = 0.000
0.000 + 2x + x2 = 0 + 5.375
2x + x2 = 0 + 5.375

Combine like terms: 0 + 5.375 = 5.375
2x + x2 = 5.375

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 5.375 + 1

Reorder the terms:
1 + 2x + x2 = 5.375 + 1

Combine like terms: 5.375 + 1 = 6.375
1 + 2x + x2 = 6.375

Factor a perfect square on the left side:
(x + 1)(x + 1) = 6.375

Calculate the square root of the right side: 2.524876235

Break this problem into two subproblems by setting 
(x + 1) equal to 2.524876235 and -2.524876235.

Subproblem 1

x + 1 = 2.524876235 Simplifying x + 1 = 2.524876235 Reorder the terms: 1 + x = 2.524876235 Solving 1 + x = 2.524876235 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 2.524876235 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.524876235 + -1 x = 2.524876235 + -1 Combine like terms: 2.524876235 + -1 = 1.524876235 x = 1.524876235 Simplifying x = 1.524876235

Subproblem 2

x + 1 = -2.524876235 Simplifying x + 1 = -2.524876235 Reorder the terms: 1 + x = -2.524876235 Solving 1 + x = -2.524876235 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -2.524876235 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.524876235 + -1 x = -2.524876235 + -1 Combine like terms: -2.524876235 + -1 = -3.524876235 x = -3.524876235 Simplifying x = -3.524876235

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.524876235, -3.524876235}

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