5x^2+78x-108=0

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Solution for 5x^2+78x-108=0 equation:


Simplifying
5x2 + 78x + -108 = 0

Reorder the terms:
-108 + 78x + 5x2 = 0

Solving
-108 + 78x + 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'.
-21.6 + 15.6x + x2 = 0

Move the constant term to the right:

Add '21.6' to each side of the equation.
-21.6 + 15.6x + 21.6 + x2 = 0 + 21.6

Reorder the terms:
-21.6 + 21.6 + 15.6x + x2 = 0 + 21.6

Combine like terms: -21.6 + 21.6 = 0.0
0.0 + 15.6x + x2 = 0 + 21.6
15.6x + x2 = 0 + 21.6

Combine like terms: 0 + 21.6 = 21.6
15.6x + x2 = 21.6

The x term is 15.6x.  Take half its coefficient (7.8).
Square it (60.84) and add it to both sides.

Add '60.84' to each side of the equation.
15.6x + 60.84 + x2 = 21.6 + 60.84

Reorder the terms:
60.84 + 15.6x + x2 = 21.6 + 60.84

Combine like terms: 21.6 + 60.84 = 82.44
60.84 + 15.6x + x2 = 82.44

Factor a perfect square on the left side:
(x + 7.8)(x + 7.8) = 82.44

Calculate the square root of the right side: 9.07964757

Break this problem into two subproblems by setting 
(x + 7.8) equal to 9.07964757 and -9.07964757.

Subproblem 1

x + 7.8 = 9.07964757 Simplifying x + 7.8 = 9.07964757 Reorder the terms: 7.8 + x = 9.07964757 Solving 7.8 + x = 9.07964757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.8' to each side of the equation. 7.8 + -7.8 + x = 9.07964757 + -7.8 Combine like terms: 7.8 + -7.8 = 0.0 0.0 + x = 9.07964757 + -7.8 x = 9.07964757 + -7.8 Combine like terms: 9.07964757 + -7.8 = 1.27964757 x = 1.27964757 Simplifying x = 1.27964757

Subproblem 2

x + 7.8 = -9.07964757 Simplifying x + 7.8 = -9.07964757 Reorder the terms: 7.8 + x = -9.07964757 Solving 7.8 + x = -9.07964757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.8' to each side of the equation. 7.8 + -7.8 + x = -9.07964757 + -7.8 Combine like terms: 7.8 + -7.8 = 0.0 0.0 + x = -9.07964757 + -7.8 x = -9.07964757 + -7.8 Combine like terms: -9.07964757 + -7.8 = -16.87964757 x = -16.87964757 Simplifying x = -16.87964757

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.27964757, -16.87964757}

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