3x^2+15x-80=0

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Solution for 3x^2+15x-80=0 equation:


Simplifying
3x2 + 15x + -80 = 0

Reorder the terms:
-80 + 15x + 3x2 = 0

Solving
-80 + 15x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-26.66666667 + 5x + x2 = 0

Move the constant term to the right:

Add '26.66666667' to each side of the equation.
-26.66666667 + 5x + 26.66666667 + x2 = 0 + 26.66666667

Reorder the terms:
-26.66666667 + 26.66666667 + 5x + x2 = 0 + 26.66666667

Combine like terms: -26.66666667 + 26.66666667 = 0.00000000
0.00000000 + 5x + x2 = 0 + 26.66666667
5x + x2 = 0 + 26.66666667

Combine like terms: 0 + 26.66666667 = 26.66666667
5x + x2 = 26.66666667

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 26.66666667 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 26.66666667 + 6.25

Combine like terms: 26.66666667 + 6.25 = 32.91666667
6.25 + 5x + x2 = 32.91666667

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 32.91666667

Calculate the square root of the right side: 5.737304826

Break this problem into two subproblems by setting 
(x + 2.5) equal to 5.737304826 and -5.737304826.

Subproblem 1

x + 2.5 = 5.737304826 Simplifying x + 2.5 = 5.737304826 Reorder the terms: 2.5 + x = 5.737304826 Solving 2.5 + x = 5.737304826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 5.737304826 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 5.737304826 + -2.5 x = 5.737304826 + -2.5 Combine like terms: 5.737304826 + -2.5 = 3.237304826 x = 3.237304826 Simplifying x = 3.237304826

Subproblem 2

x + 2.5 = -5.737304826 Simplifying x + 2.5 = -5.737304826 Reorder the terms: 2.5 + x = -5.737304826 Solving 2.5 + x = -5.737304826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -5.737304826 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -5.737304826 + -2.5 x = -5.737304826 + -2.5 Combine like terms: -5.737304826 + -2.5 = -8.237304826 x = -8.237304826 Simplifying x = -8.237304826

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.237304826, -8.237304826}

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