0.2x^2-0.3x-3.5=0

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Solution for 0.2x^2-0.3x-3.5=0 equation:


Simplifying
0.2x2 + -0.3x + -3.5 = 0

Reorder the terms:
-3.5 + -0.3x + 0.2x2 = 0

Solving
-3.5 + -0.3x + 0.2x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.2'.
-17.5 + -1.5x + x2 = 0

Move the constant term to the right:

Add '17.5' to each side of the equation.
-17.5 + -1.5x + 17.5 + x2 = 0 + 17.5

Reorder the terms:
-17.5 + 17.5 + -1.5x + x2 = 0 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + -1.5x + x2 = 0 + 17.5
-1.5x + x2 = 0 + 17.5

Combine like terms: 0 + 17.5 = 17.5
-1.5x + x2 = 17.5

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = 17.5 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 17.5 + 0.5625

Combine like terms: 17.5 + 0.5625 = 18.0625
0.5625 + -1.5x + x2 = 18.0625

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 18.0625

Calculate the square root of the right side: 4.25

Break this problem into two subproblems by setting 
(x + -0.75) equal to 4.25 and -4.25.

Subproblem 1

x + -0.75 = 4.25 Simplifying x + -0.75 = 4.25 Reorder the terms: -0.75 + x = 4.25 Solving -0.75 + x = 4.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 4.25 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 4.25 + 0.75 x = 4.25 + 0.75 Combine like terms: 4.25 + 0.75 = 5 x = 5 Simplifying x = 5

Subproblem 2

x + -0.75 = -4.25 Simplifying x + -0.75 = -4.25 Reorder the terms: -0.75 + x = -4.25 Solving -0.75 + x = -4.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -4.25 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -4.25 + 0.75 x = -4.25 + 0.75 Combine like terms: -4.25 + 0.75 = -3.5 x = -3.5 Simplifying x = -3.5

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5, -3.5}

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