-16x^2+.003x+3=0

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Solution for -16x^2+.003x+3=0 equation:


Simplifying
-16x2 + 0.003x + 3 = 0

Reorder the terms:
3 + 0.003x + -16x2 = 0

Solving
3 + 0.003x + -16x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
-0.1875 + -0.0001875x + x2 = 0

Move the constant term to the right:

Add '0.1875' to each side of the equation.
-0.1875 + -0.0001875x + 0.1875 + x2 = 0 + 0.1875

Reorder the terms:
-0.1875 + 0.1875 + -0.0001875x + x2 = 0 + 0.1875

Combine like terms: -0.1875 + 0.1875 = 0.0000
0.0000 + -0.0001875x + x2 = 0 + 0.1875
-0.0001875x + x2 = 0 + 0.1875

Combine like terms: 0 + 0.1875 = 0.1875
-0.0001875x + x2 = 0.1875

The x term is -0.0001875x.  Take half its coefficient (-0.00009375).
Square it (0.0000000087890625) and add it to both sides.

Add '0.0000000087890625' to each side of the equation.
-0.0001875x + 0.0000000087890625 + x2 = 0.1875 + 0.0000000087890625

Reorder the terms:
0.0000000087890625 + -0.0001875x + x2 = 0.1875 + 0.0000000087890625

Combine like terms: 0.1875 + 0.0000000087890625 = 0.1875000087890625
0.0000000087890625 + -0.0001875x + x2 = 0.1875000087890625

Factor a perfect square on the left side:
(x + -0.00009375)(x + -0.00009375) = 0.1875000087890625

Calculate the square root of the right side: 0.433012712

Break this problem into two subproblems by setting 
(x + -0.00009375) equal to 0.433012712 and -0.433012712.

Subproblem 1

x + -0.00009375 = 0.433012712 Simplifying x + -0.00009375 = 0.433012712 Reorder the terms: -0.00009375 + x = 0.433012712 Solving -0.00009375 + x = 0.433012712 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.00009375' to each side of the equation. -0.00009375 + 0.00009375 + x = 0.433012712 + 0.00009375 Combine like terms: -0.00009375 + 0.00009375 = 0.00000000 0.00000000 + x = 0.433012712 + 0.00009375 x = 0.433012712 + 0.00009375 Combine like terms: 0.433012712 + 0.00009375 = 0.433106462 x = 0.433106462 Simplifying x = 0.433106462

Subproblem 2

x + -0.00009375 = -0.433012712 Simplifying x + -0.00009375 = -0.433012712 Reorder the terms: -0.00009375 + x = -0.433012712 Solving -0.00009375 + x = -0.433012712 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.00009375' to each side of the equation. -0.00009375 + 0.00009375 + x = -0.433012712 + 0.00009375 Combine like terms: -0.00009375 + 0.00009375 = 0.00000000 0.00000000 + x = -0.433012712 + 0.00009375 x = -0.433012712 + 0.00009375 Combine like terms: -0.433012712 + 0.00009375 = -0.432918962 x = -0.432918962 Simplifying x = -0.432918962

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.433106462, -0.432918962}

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