5x^2+19x-720=0

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Solution for 5x^2+19x-720=0 equation:


Simplifying
5x2 + 19x + -720 = 0

Reorder the terms:
-720 + 19x + 5x2 = 0

Solving
-720 + 19x + 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'.
-144 + 3.8x + x2 = 0

Move the constant term to the right:

Add '144' to each side of the equation.
-144 + 3.8x + 144 + x2 = 0 + 144

Reorder the terms:
-144 + 144 + 3.8x + x2 = 0 + 144

Combine like terms: -144 + 144 = 0
0 + 3.8x + x2 = 0 + 144
3.8x + x2 = 0 + 144

Combine like terms: 0 + 144 = 144
3.8x + x2 = 144

The x term is 3.8x.  Take half its coefficient (1.9).
Square it (3.61) and add it to both sides.

Add '3.61' to each side of the equation.
3.8x + 3.61 + x2 = 144 + 3.61

Reorder the terms:
3.61 + 3.8x + x2 = 144 + 3.61

Combine like terms: 144 + 3.61 = 147.61
3.61 + 3.8x + x2 = 147.61

Factor a perfect square on the left side:
(x + 1.9)(x + 1.9) = 147.61

Calculate the square root of the right side: 12.149485586

Break this problem into two subproblems by setting 
(x + 1.9) equal to 12.149485586 and -12.149485586.

Subproblem 1

x + 1.9 = 12.149485586 Simplifying x + 1.9 = 12.149485586 Reorder the terms: 1.9 + x = 12.149485586 Solving 1.9 + x = 12.149485586 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.9' to each side of the equation. 1.9 + -1.9 + x = 12.149485586 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + x = 12.149485586 + -1.9 x = 12.149485586 + -1.9 Combine like terms: 12.149485586 + -1.9 = 10.249485586 x = 10.249485586 Simplifying x = 10.249485586

Subproblem 2

x + 1.9 = -12.149485586 Simplifying x + 1.9 = -12.149485586 Reorder the terms: 1.9 + x = -12.149485586 Solving 1.9 + x = -12.149485586 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.9' to each side of the equation. 1.9 + -1.9 + x = -12.149485586 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + x = -12.149485586 + -1.9 x = -12.149485586 + -1.9 Combine like terms: -12.149485586 + -1.9 = -14.049485586 x = -14.049485586 Simplifying x = -14.049485586

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.249485586, -14.049485586}

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