x^2+3x-800=0

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Solution for x^2+3x-800=0 equation:


Simplifying
x2 + 3x + -800 = 0

Reorder the terms:
-800 + 3x + x2 = 0

Solving
-800 + 3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '800' to each side of the equation.
-800 + 3x + 800 + x2 = 0 + 800

Reorder the terms:
-800 + 800 + 3x + x2 = 0 + 800

Combine like terms: -800 + 800 = 0
0 + 3x + x2 = 0 + 800
3x + x2 = 0 + 800

Combine like terms: 0 + 800 = 800
3x + x2 = 800

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 800 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 800 + 2.25

Combine like terms: 800 + 2.25 = 802.25
2.25 + 3x + x2 = 802.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 802.25

Calculate the square root of the right side: 28.324018077

Break this problem into two subproblems by setting 
(x + 1.5) equal to 28.324018077 and -28.324018077.

Subproblem 1

x + 1.5 = 28.324018077 Simplifying x + 1.5 = 28.324018077 Reorder the terms: 1.5 + x = 28.324018077 Solving 1.5 + x = 28.324018077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 28.324018077 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 28.324018077 + -1.5 x = 28.324018077 + -1.5 Combine like terms: 28.324018077 + -1.5 = 26.824018077 x = 26.824018077 Simplifying x = 26.824018077

Subproblem 2

x + 1.5 = -28.324018077 Simplifying x + 1.5 = -28.324018077 Reorder the terms: 1.5 + x = -28.324018077 Solving 1.5 + x = -28.324018077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -28.324018077 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -28.324018077 + -1.5 x = -28.324018077 + -1.5 Combine like terms: -28.324018077 + -1.5 = -29.824018077 x = -29.824018077 Simplifying x = -29.824018077

Solution

The solution to the problem is based on the solutions from the subproblems. x = {26.824018077, -29.824018077}

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