5x^2+77x-6=0

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Solution for 5x^2+77x-6=0 equation:


Simplifying
5x2 + 77x + -6 = 0

Reorder the terms:
-6 + 77x + 5x2 = 0

Solving
-6 + 77x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-1.2 + 15.4x + x2 = 0

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + 15.4x + 1.2 + x2 = 0 + 1.2

Reorder the terms:
-1.2 + 1.2 + 15.4x + x2 = 0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + 15.4x + x2 = 0 + 1.2
15.4x + x2 = 0 + 1.2

Combine like terms: 0 + 1.2 = 1.2
15.4x + x2 = 1.2

The x term is 15.4x.  Take half its coefficient (7.7).
Square it (59.29) and add it to both sides.

Add '59.29' to each side of the equation.
15.4x + 59.29 + x2 = 1.2 + 59.29

Reorder the terms:
59.29 + 15.4x + x2 = 1.2 + 59.29

Combine like terms: 1.2 + 59.29 = 60.49
59.29 + 15.4x + x2 = 60.49

Factor a perfect square on the left side:
(x + 7.7)(x + 7.7) = 60.49

Calculate the square root of the right side: 7.777531742

Break this problem into two subproblems by setting 
(x + 7.7) equal to 7.777531742 and -7.777531742.

Subproblem 1

x + 7.7 = 7.777531742 Simplifying x + 7.7 = 7.777531742 Reorder the terms: 7.7 + x = 7.777531742 Solving 7.7 + x = 7.777531742 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.7' to each side of the equation. 7.7 + -7.7 + x = 7.777531742 + -7.7 Combine like terms: 7.7 + -7.7 = 0.0 0.0 + x = 7.777531742 + -7.7 x = 7.777531742 + -7.7 Combine like terms: 7.777531742 + -7.7 = 0.077531742 x = 0.077531742 Simplifying x = 0.077531742

Subproblem 2

x + 7.7 = -7.777531742 Simplifying x + 7.7 = -7.777531742 Reorder the terms: 7.7 + x = -7.777531742 Solving 7.7 + x = -7.777531742 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.7' to each side of the equation. 7.7 + -7.7 + x = -7.777531742 + -7.7 Combine like terms: 7.7 + -7.7 = 0.0 0.0 + x = -7.777531742 + -7.7 x = -7.777531742 + -7.7 Combine like terms: -7.777531742 + -7.7 = -15.477531742 x = -15.477531742 Simplifying x = -15.477531742

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.077531742, -15.477531742}

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