5x^2-8x-67=-2

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Solution for 5x^2-8x-67=-2 equation:


Simplifying
5x2 + -8x + -67 = -2

Reorder the terms:
-67 + -8x + 5x2 = -2

Solving
-67 + -8x + 5x2 = -2

Solving for variable 'x'.

Reorder the terms:
-67 + 2 + -8x + 5x2 = -2 + 2

Combine like terms: -67 + 2 = -65
-65 + -8x + 5x2 = -2 + 2

Combine like terms: -2 + 2 = 0
-65 + -8x + 5x2 = 0

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

Divide each side by '5'.
-13 + -1.6x + x2 = 0

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + -1.6x + 13 + x2 = 0 + 13

Reorder the terms:
-13 + 13 + -1.6x + x2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -1.6x + x2 = 0 + 13
-1.6x + x2 = 0 + 13

Combine like terms: 0 + 13 = 13
-1.6x + x2 = 13

The x term is -1.6x.  Take half its coefficient (-0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
-1.6x + 0.64 + x2 = 13 + 0.64

Reorder the terms:
0.64 + -1.6x + x2 = 13 + 0.64

Combine like terms: 13 + 0.64 = 13.64
0.64 + -1.6x + x2 = 13.64

Factor a perfect square on the left side:
(x + -0.8)(x + -0.8) = 13.64

Calculate the square root of the right side: 3.693237063

Break this problem into two subproblems by setting 
(x + -0.8) equal to 3.693237063 and -3.693237063.

Subproblem 1

x + -0.8 = 3.693237063 Simplifying x + -0.8 = 3.693237063 Reorder the terms: -0.8 + x = 3.693237063 Solving -0.8 + x = 3.693237063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = 3.693237063 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 3.693237063 + 0.8 x = 3.693237063 + 0.8 Combine like terms: 3.693237063 + 0.8 = 4.493237063 x = 4.493237063 Simplifying x = 4.493237063

Subproblem 2

x + -0.8 = -3.693237063 Simplifying x + -0.8 = -3.693237063 Reorder the terms: -0.8 + x = -3.693237063 Solving -0.8 + x = -3.693237063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = -3.693237063 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -3.693237063 + 0.8 x = -3.693237063 + 0.8 Combine like terms: -3.693237063 + 0.8 = -2.893237063 x = -2.893237063 Simplifying x = -2.893237063

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.493237063, -2.893237063}

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