0=-2.5x^2+10x+8

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Solution for 0=-2.5x^2+10x+8 equation:


Simplifying
0 = -2.5x2 + 10x + 8

Reorder the terms:
0 = 8 + 10x + -2.5x2

Solving
0 = 8 + 10x + -2.5x2

Solving for variable 'x'.

Combine like terms: 0 + -8 = -8
-8 + -10x + 2.5x2 = 8 + 10x + -2.5x2 + -8 + -10x + 2.5x2

Reorder the terms:
-8 + -10x + 2.5x2 = 8 + -8 + 10x + -10x + -2.5x2 + 2.5x2

Combine like terms: 8 + -8 = 0
-8 + -10x + 2.5x2 = 0 + 10x + -10x + -2.5x2 + 2.5x2
-8 + -10x + 2.5x2 = 10x + -10x + -2.5x2 + 2.5x2

Combine like terms: 10x + -10x = 0
-8 + -10x + 2.5x2 = 0 + -2.5x2 + 2.5x2
-8 + -10x + 2.5x2 = -2.5x2 + 2.5x2

Combine like terms: -2.5x2 + 2.5x2 = 0.0
-8 + -10x + 2.5x2 = 0.0

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

Divide each side by '2.5'.
-3.2 + -4x + x2 = 0

Move the constant term to the right:

Add '3.2' to each side of the equation.
-3.2 + -4x + 3.2 + x2 = 0 + 3.2

Reorder the terms:
-3.2 + 3.2 + -4x + x2 = 0 + 3.2

Combine like terms: -3.2 + 3.2 = 0.0
0.0 + -4x + x2 = 0 + 3.2
-4x + x2 = 0 + 3.2

Combine like terms: 0 + 3.2 = 3.2
-4x + x2 = 3.2

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 3.2 + 4

Reorder the terms:
4 + -4x + x2 = 3.2 + 4

Combine like terms: 3.2 + 4 = 7.2
4 + -4x + x2 = 7.2

Factor a perfect square on the left side:
(x + -2)(x + -2) = 7.2

Calculate the square root of the right side: 2.683281573

Break this problem into two subproblems by setting 
(x + -2) equal to 2.683281573 and -2.683281573.

Subproblem 1

x + -2 = 2.683281573 Simplifying x + -2 = 2.683281573 Reorder the terms: -2 + x = 2.683281573 Solving -2 + x = 2.683281573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 2.683281573 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.683281573 + 2 x = 2.683281573 + 2 Combine like terms: 2.683281573 + 2 = 4.683281573 x = 4.683281573 Simplifying x = 4.683281573

Subproblem 2

x + -2 = -2.683281573 Simplifying x + -2 = -2.683281573 Reorder the terms: -2 + x = -2.683281573 Solving -2 + x = -2.683281573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -2.683281573 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.683281573 + 2 x = -2.683281573 + 2 Combine like terms: -2.683281573 + 2 = -0.683281573 x = -0.683281573 Simplifying x = -0.683281573

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.683281573, -0.683281573}

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