x^2-3x=80

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Solution for x^2-3x=80 equation:


Simplifying
x2 + -3x = 80

Reorder the terms:
-3x + x2 = 80

Solving
-3x + x2 = 80

Solving for variable 'x'.

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

Combine like terms: 80 + -80 = 0
-80 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '80' to each side of the equation.
-80 + -3x + 80 + x2 = 0 + 80

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

Combine like terms: -80 + 80 = 0
0 + -3x + x2 = 0 + 80
-3x + x2 = 0 + 80

Combine like terms: 0 + 80 = 80
-3x + x2 = 80

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 = 80 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 80 + 2.25

Combine like terms: 80 + 2.25 = 82.25
2.25 + -3x + x2 = 82.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 82.25

Calculate the square root of the right side: 9.069178574

Break this problem into two subproblems by setting 
(x + -1.5) equal to 9.069178574 and -9.069178574.

Subproblem 1

x + -1.5 = 9.069178574 Simplifying x + -1.5 = 9.069178574 Reorder the terms: -1.5 + x = 9.069178574 Solving -1.5 + x = 9.069178574 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 = 9.069178574 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 9.069178574 + 1.5 x = 9.069178574 + 1.5 Combine like terms: 9.069178574 + 1.5 = 10.569178574 x = 10.569178574 Simplifying x = 10.569178574

Subproblem 2

x + -1.5 = -9.069178574 Simplifying x + -1.5 = -9.069178574 Reorder the terms: -1.5 + x = -9.069178574 Solving -1.5 + x = -9.069178574 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 = -9.069178574 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -9.069178574 + 1.5 x = -9.069178574 + 1.5 Combine like terms: -9.069178574 + 1.5 = -7.569178574 x = -7.569178574 Simplifying x = -7.569178574

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.569178574, -7.569178574}

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