8x^2-16x-62=-9

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Solution for 8x^2-16x-62=-9 equation:


Simplifying
8x2 + -16x + -62 = -9

Reorder the terms:
-62 + -16x + 8x2 = -9

Solving
-62 + -16x + 8x2 = -9

Solving for variable 'x'.

Reorder the terms:
-62 + 9 + -16x + 8x2 = -9 + 9

Combine like terms: -62 + 9 = -53
-53 + -16x + 8x2 = -9 + 9

Combine like terms: -9 + 9 = 0
-53 + -16x + 8x2 = 0

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

Divide each side by '8'.
-6.625 + -2x + x2 = 0

Move the constant term to the right:

Add '6.625' to each side of the equation.
-6.625 + -2x + 6.625 + x2 = 0 + 6.625

Reorder the terms:
-6.625 + 6.625 + -2x + x2 = 0 + 6.625

Combine like terms: -6.625 + 6.625 = 0.000
0.000 + -2x + x2 = 0 + 6.625
-2x + x2 = 0 + 6.625

Combine like terms: 0 + 6.625 = 6.625
-2x + x2 = 6.625

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 = 6.625 + 1

Reorder the terms:
1 + -2x + x2 = 6.625 + 1

Combine like terms: 6.625 + 1 = 7.625
1 + -2x + x2 = 7.625

Factor a perfect square on the left side:
(x + -1)(x + -1) = 7.625

Calculate the square root of the right side: 2.761340254

Break this problem into two subproblems by setting 
(x + -1) equal to 2.761340254 and -2.761340254.

Subproblem 1

x + -1 = 2.761340254 Simplifying x + -1 = 2.761340254 Reorder the terms: -1 + x = 2.761340254 Solving -1 + x = 2.761340254 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 = 2.761340254 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.761340254 + 1 x = 2.761340254 + 1 Combine like terms: 2.761340254 + 1 = 3.761340254 x = 3.761340254 Simplifying x = 3.761340254

Subproblem 2

x + -1 = -2.761340254 Simplifying x + -1 = -2.761340254 Reorder the terms: -1 + x = -2.761340254 Solving -1 + x = -2.761340254 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 = -2.761340254 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.761340254 + 1 x = -2.761340254 + 1 Combine like terms: -2.761340254 + 1 = -1.761340254 x = -1.761340254 Simplifying x = -1.761340254

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.761340254, -1.761340254}

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