40=-16x^2+122x+3

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Solution for 40=-16x^2+122x+3 equation:


Simplifying
40 = -16x2 + 122x + 3

Reorder the terms:
40 = 3 + 122x + -16x2

Solving
40 = 3 + 122x + -16x2

Solving for variable 'x'.

Combine like terms: 40 + -3 = 37
37 + -122x + 16x2 = 3 + 122x + -16x2 + -3 + -122x + 16x2

Reorder the terms:
37 + -122x + 16x2 = 3 + -3 + 122x + -122x + -16x2 + 16x2

Combine like terms: 3 + -3 = 0
37 + -122x + 16x2 = 0 + 122x + -122x + -16x2 + 16x2
37 + -122x + 16x2 = 122x + -122x + -16x2 + 16x2

Combine like terms: 122x + -122x = 0
37 + -122x + 16x2 = 0 + -16x2 + 16x2
37 + -122x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
37 + -122x + 16x2 = 0

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

Divide each side by '16'.
2.3125 + -7.625x + x2 = 0

Move the constant term to the right:

Add '-2.3125' to each side of the equation.
2.3125 + -7.625x + -2.3125 + x2 = 0 + -2.3125

Reorder the terms:
2.3125 + -2.3125 + -7.625x + x2 = 0 + -2.3125

Combine like terms: 2.3125 + -2.3125 = 0.0000
0.0000 + -7.625x + x2 = 0 + -2.3125
-7.625x + x2 = 0 + -2.3125

Combine like terms: 0 + -2.3125 = -2.3125
-7.625x + x2 = -2.3125

The x term is -7.625x.  Take half its coefficient (-3.8125).
Square it (14.53515625) and add it to both sides.

Add '14.53515625' to each side of the equation.
-7.625x + 14.53515625 + x2 = -2.3125 + 14.53515625

Reorder the terms:
14.53515625 + -7.625x + x2 = -2.3125 + 14.53515625

Combine like terms: -2.3125 + 14.53515625 = 12.22265625
14.53515625 + -7.625x + x2 = 12.22265625

Factor a perfect square on the left side:
(x + -3.8125)(x + -3.8125) = 12.22265625

Calculate the square root of the right side: 3.496091568

Break this problem into two subproblems by setting 
(x + -3.8125) equal to 3.496091568 and -3.496091568.

Subproblem 1

x + -3.8125 = 3.496091568 Simplifying x + -3.8125 = 3.496091568 Reorder the terms: -3.8125 + x = 3.496091568 Solving -3.8125 + x = 3.496091568 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.8125' to each side of the equation. -3.8125 + 3.8125 + x = 3.496091568 + 3.8125 Combine like terms: -3.8125 + 3.8125 = 0.0000 0.0000 + x = 3.496091568 + 3.8125 x = 3.496091568 + 3.8125 Combine like terms: 3.496091568 + 3.8125 = 7.308591568 x = 7.308591568 Simplifying x = 7.308591568

Subproblem 2

x + -3.8125 = -3.496091568 Simplifying x + -3.8125 = -3.496091568 Reorder the terms: -3.8125 + x = -3.496091568 Solving -3.8125 + x = -3.496091568 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.8125' to each side of the equation. -3.8125 + 3.8125 + x = -3.496091568 + 3.8125 Combine like terms: -3.8125 + 3.8125 = 0.0000 0.0000 + x = -3.496091568 + 3.8125 x = -3.496091568 + 3.8125 Combine like terms: -3.496091568 + 3.8125 = 0.316408432 x = 0.316408432 Simplifying x = 0.316408432

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.308591568, 0.316408432}

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