5x^2+14x-180=0

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Solution for 5x^2+14x-180=0 equation:


Simplifying
5x2 + 14x + -180 = 0

Reorder the terms:
-180 + 14x + 5x2 = 0

Solving
-180 + 14x + 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'.
-36 + 2.8x + x2 = 0

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + 2.8x + 36 + x2 = 0 + 36

Reorder the terms:
-36 + 36 + 2.8x + x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 2.8x + x2 = 0 + 36
2.8x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
2.8x + x2 = 36

The x term is 2.8x.  Take half its coefficient (1.4).
Square it (1.96) and add it to both sides.

Add '1.96' to each side of the equation.
2.8x + 1.96 + x2 = 36 + 1.96

Reorder the terms:
1.96 + 2.8x + x2 = 36 + 1.96

Combine like terms: 36 + 1.96 = 37.96
1.96 + 2.8x + x2 = 37.96

Factor a perfect square on the left side:
(x + 1.4)(x + 1.4) = 37.96

Calculate the square root of the right side: 6.16116872

Break this problem into two subproblems by setting 
(x + 1.4) equal to 6.16116872 and -6.16116872.

Subproblem 1

x + 1.4 = 6.16116872 Simplifying x + 1.4 = 6.16116872 Reorder the terms: 1.4 + x = 6.16116872 Solving 1.4 + x = 6.16116872 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + x = 6.16116872 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = 6.16116872 + -1.4 x = 6.16116872 + -1.4 Combine like terms: 6.16116872 + -1.4 = 4.76116872 x = 4.76116872 Simplifying x = 4.76116872

Subproblem 2

x + 1.4 = -6.16116872 Simplifying x + 1.4 = -6.16116872 Reorder the terms: 1.4 + x = -6.16116872 Solving 1.4 + x = -6.16116872 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + x = -6.16116872 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = -6.16116872 + -1.4 x = -6.16116872 + -1.4 Combine like terms: -6.16116872 + -1.4 = -7.56116872 x = -7.56116872 Simplifying x = -7.56116872

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.76116872, -7.56116872}

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