8x-2x^2=3

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Solution for 8x-2x^2=3 equation:


Simplifying
8x + -2x2 = 3

Solving
8x + -2x2 = 3

Solving for variable 'x'.

Reorder the terms:
-3 + 8x + -2x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 8x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
1.5 + -4x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -4x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -4x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -4x + x2 = 0 + -1.5
-4x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-4x + x2 = -1.5

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 = -1.5 + 4

Reorder the terms:
4 + -4x + x2 = -1.5 + 4

Combine like terms: -1.5 + 4 = 2.5
4 + -4x + x2 = 2.5

Factor a perfect square on the left side:
(x + -2)(x + -2) = 2.5

Calculate the square root of the right side: 1.58113883

Break this problem into two subproblems by setting 
(x + -2) equal to 1.58113883 and -1.58113883.

Subproblem 1

x + -2 = 1.58113883 Simplifying x + -2 = 1.58113883 Reorder the terms: -2 + x = 1.58113883 Solving -2 + x = 1.58113883 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 = 1.58113883 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.58113883 + 2 x = 1.58113883 + 2 Combine like terms: 1.58113883 + 2 = 3.58113883 x = 3.58113883 Simplifying x = 3.58113883

Subproblem 2

x + -2 = -1.58113883 Simplifying x + -2 = -1.58113883 Reorder the terms: -2 + x = -1.58113883 Solving -2 + x = -1.58113883 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 = -1.58113883 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.58113883 + 2 x = -1.58113883 + 2 Combine like terms: -1.58113883 + 2 = 0.41886117 x = 0.41886117 Simplifying x = 0.41886117

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.58113883, 0.41886117}

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