0=-0.8x^2-2.4x+6

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Solution for 0=-0.8x^2-2.4x+6 equation:


Simplifying
0 = -0.8x2 + -2.4x + 6

Reorder the terms:
0 = 6 + -2.4x + -0.8x2

Solving
0 = 6 + -2.4x + -0.8x2

Solving for variable 'x'.

Combine like terms: 0 + -6 = -6
-6 + 2.4x + 0.8x2 = 6 + -2.4x + -0.8x2 + -6 + 2.4x + 0.8x2

Reorder the terms:
-6 + 2.4x + 0.8x2 = 6 + -6 + -2.4x + 2.4x + -0.8x2 + 0.8x2

Combine like terms: 6 + -6 = 0
-6 + 2.4x + 0.8x2 = 0 + -2.4x + 2.4x + -0.8x2 + 0.8x2
-6 + 2.4x + 0.8x2 = -2.4x + 2.4x + -0.8x2 + 0.8x2

Combine like terms: -2.4x + 2.4x = 0.0
-6 + 2.4x + 0.8x2 = 0.0 + -0.8x2 + 0.8x2
-6 + 2.4x + 0.8x2 = -0.8x2 + 0.8x2

Combine like terms: -0.8x2 + 0.8x2 = 0.0
-6 + 2.4x + 0.8x2 = 0.0

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

Divide each side by '0.8'.
-7.5 + 3x + x2 = 0

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + 3x + 7.5 + x2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + 3x + x2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + 3x + x2 = 0 + 7.5
3x + x2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
3x + x2 = 7.5

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 = 7.5 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 7.5 + 2.25

Combine like terms: 7.5 + 2.25 = 9.75
2.25 + 3x + x2 = 9.75

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 9.75

Calculate the square root of the right side: 3.122498999

Break this problem into two subproblems by setting 
(x + 1.5) equal to 3.122498999 and -3.122498999.

Subproblem 1

x + 1.5 = 3.122498999 Simplifying x + 1.5 = 3.122498999 Reorder the terms: 1.5 + x = 3.122498999 Solving 1.5 + x = 3.122498999 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 = 3.122498999 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 3.122498999 + -1.5 x = 3.122498999 + -1.5 Combine like terms: 3.122498999 + -1.5 = 1.622498999 x = 1.622498999 Simplifying x = 1.622498999

Subproblem 2

x + 1.5 = -3.122498999 Simplifying x + 1.5 = -3.122498999 Reorder the terms: 1.5 + x = -3.122498999 Solving 1.5 + x = -3.122498999 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 = -3.122498999 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -3.122498999 + -1.5 x = -3.122498999 + -1.5 Combine like terms: -3.122498999 + -1.5 = -4.622498999 x = -4.622498999 Simplifying x = -4.622498999

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.622498999, -4.622498999}

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