-16x^2+9.8x+3=0

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Solution for -16x^2+9.8x+3=0 equation:


Simplifying
-16x2 + 9.8x + 3 = 0

Reorder the terms:
3 + 9.8x + -16x2 = 0

Solving
3 + 9.8x + -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 + -0.6125x + x2 = 0

Move the constant term to the right:

Add '0.1875' to each side of the equation.
-0.1875 + -0.6125x + 0.1875 + x2 = 0 + 0.1875

Reorder the terms:
-0.1875 + 0.1875 + -0.6125x + x2 = 0 + 0.1875

Combine like terms: -0.1875 + 0.1875 = 0.0000
0.0000 + -0.6125x + x2 = 0 + 0.1875
-0.6125x + x2 = 0 + 0.1875

Combine like terms: 0 + 0.1875 = 0.1875
-0.6125x + x2 = 0.1875

The x term is -0.6125x.  Take half its coefficient (-0.30625).
Square it (0.0937890625) and add it to both sides.

Add '0.0937890625' to each side of the equation.
-0.6125x + 0.0937890625 + x2 = 0.1875 + 0.0937890625

Reorder the terms:
0.0937890625 + -0.6125x + x2 = 0.1875 + 0.0937890625

Combine like terms: 0.1875 + 0.0937890625 = 0.2812890625
0.0937890625 + -0.6125x + x2 = 0.2812890625

Factor a perfect square on the left side:
(x + -0.30625)(x + -0.30625) = 0.2812890625

Calculate the square root of the right side: 0.530366913

Break this problem into two subproblems by setting 
(x + -0.30625) equal to 0.530366913 and -0.530366913.

Subproblem 1

x + -0.30625 = 0.530366913 Simplifying x + -0.30625 = 0.530366913 Reorder the terms: -0.30625 + x = 0.530366913 Solving -0.30625 + x = 0.530366913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.30625' to each side of the equation. -0.30625 + 0.30625 + x = 0.530366913 + 0.30625 Combine like terms: -0.30625 + 0.30625 = 0.00000 0.00000 + x = 0.530366913 + 0.30625 x = 0.530366913 + 0.30625 Combine like terms: 0.530366913 + 0.30625 = 0.836616913 x = 0.836616913 Simplifying x = 0.836616913

Subproblem 2

x + -0.30625 = -0.530366913 Simplifying x + -0.30625 = -0.530366913 Reorder the terms: -0.30625 + x = -0.530366913 Solving -0.30625 + x = -0.530366913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.30625' to each side of the equation. -0.30625 + 0.30625 + x = -0.530366913 + 0.30625 Combine like terms: -0.30625 + 0.30625 = 0.00000 0.00000 + x = -0.530366913 + 0.30625 x = -0.530366913 + 0.30625 Combine like terms: -0.530366913 + 0.30625 = -0.224116913 x = -0.224116913 Simplifying x = -0.224116913

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.836616913, -0.224116913}

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