-3-8x+4x^2=0

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Solution for -3-8x+4x^2=0 equation:


Simplifying
-3 + -8x + 4x2 = 0

Solving
-3 + -8x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-0.75 + -2x + x2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + -2x + 0.75 + x2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + -2x + x2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + -2x + x2 = 0 + 0.75
-2x + x2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
-2x + x2 = 0.75

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 0.75 + 1

Reorder the terms:
1 + -2x + x2 = 0.75 + 1

Combine like terms: 0.75 + 1 = 1.75
1 + -2x + x2 = 1.75

Factor a perfect square on the left side:
(x + -1)(x + -1) = 1.75

Calculate the square root of the right side: 1.322875656

Break this problem into two subproblems by setting 
(x + -1) equal to 1.322875656 and -1.322875656.

Subproblem 1

x + -1 = 1.322875656 Simplifying x + -1 = 1.322875656 Reorder the terms: -1 + x = 1.322875656 Solving -1 + x = 1.322875656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.322875656 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.322875656 + 1 x = 1.322875656 + 1 Combine like terms: 1.322875656 + 1 = 2.322875656 x = 2.322875656 Simplifying x = 2.322875656

Subproblem 2

x + -1 = -1.322875656 Simplifying x + -1 = -1.322875656 Reorder the terms: -1 + x = -1.322875656 Solving -1 + x = -1.322875656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.322875656 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.322875656 + 1 x = -1.322875656 + 1 Combine like terms: -1.322875656 + 1 = -0.322875656 x = -0.322875656 Simplifying x = -0.322875656

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.322875656, -0.322875656}

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