-16x^2+40x+3=0

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Solution for -16x^2+40x+3=0 equation:


Simplifying
-16x2 + 40x + 3 = 0

Reorder the terms:
3 + 40x + -16x2 = 0

Solving
3 + 40x + -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 + -2.5x + x2 = 0

Move the constant term to the right:

Add '0.1875' to each side of the equation.
-0.1875 + -2.5x + 0.1875 + x2 = 0 + 0.1875

Reorder the terms:
-0.1875 + 0.1875 + -2.5x + x2 = 0 + 0.1875

Combine like terms: -0.1875 + 0.1875 = 0.0000
0.0000 + -2.5x + x2 = 0 + 0.1875
-2.5x + x2 = 0 + 0.1875

Combine like terms: 0 + 0.1875 = 0.1875
-2.5x + x2 = 0.1875

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = 0.1875 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = 0.1875 + 1.5625

Combine like terms: 0.1875 + 1.5625 = 1.75
1.5625 + -2.5x + x2 = 1.75

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 1.75

Calculate the square root of the right side: 1.322875656

Break this problem into two subproblems by setting 
(x + -1.25) equal to 1.322875656 and -1.322875656.

Subproblem 1

x + -1.25 = 1.322875656 Simplifying x + -1.25 = 1.322875656 Reorder the terms: -1.25 + x = 1.322875656 Solving -1.25 + x = 1.322875656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 1.322875656 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 1.322875656 + 1.25 x = 1.322875656 + 1.25 Combine like terms: 1.322875656 + 1.25 = 2.572875656 x = 2.572875656 Simplifying x = 2.572875656

Subproblem 2

x + -1.25 = -1.322875656 Simplifying x + -1.25 = -1.322875656 Reorder the terms: -1.25 + x = -1.322875656 Solving -1.25 + x = -1.322875656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -1.322875656 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -1.322875656 + 1.25 x = -1.322875656 + 1.25 Combine like terms: -1.322875656 + 1.25 = -0.072875656 x = -0.072875656 Simplifying x = -0.072875656

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.572875656, -0.072875656}

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