0=-16x^2+60x+5

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Solution for 0=-16x^2+60x+5 equation:


Simplifying
0 = -16x2 + 60x + 5

Reorder the terms:
0 = 5 + 60x + -16x2

Solving
0 = 5 + 60x + -16x2

Solving for variable 'x'.

Combine like terms: 0 + -5 = -5
-5 + -60x + 16x2 = 5 + 60x + -16x2 + -5 + -60x + 16x2

Reorder the terms:
-5 + -60x + 16x2 = 5 + -5 + 60x + -60x + -16x2 + 16x2

Combine like terms: 5 + -5 = 0
-5 + -60x + 16x2 = 0 + 60x + -60x + -16x2 + 16x2
-5 + -60x + 16x2 = 60x + -60x + -16x2 + 16x2

Combine like terms: 60x + -60x = 0
-5 + -60x + 16x2 = 0 + -16x2 + 16x2
-5 + -60x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
-5 + -60x + 16x2 = 0

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

Divide each side by '16'.
-0.3125 + -3.75x + x2 = 0

Move the constant term to the right:

Add '0.3125' to each side of the equation.
-0.3125 + -3.75x + 0.3125 + x2 = 0 + 0.3125

Reorder the terms:
-0.3125 + 0.3125 + -3.75x + x2 = 0 + 0.3125

Combine like terms: -0.3125 + 0.3125 = 0.0000
0.0000 + -3.75x + x2 = 0 + 0.3125
-3.75x + x2 = 0 + 0.3125

Combine like terms: 0 + 0.3125 = 0.3125
-3.75x + x2 = 0.3125

The x term is -3.75x.  Take half its coefficient (-1.875).
Square it (3.515625) and add it to both sides.

Add '3.515625' to each side of the equation.
-3.75x + 3.515625 + x2 = 0.3125 + 3.515625

Reorder the terms:
3.515625 + -3.75x + x2 = 0.3125 + 3.515625

Combine like terms: 0.3125 + 3.515625 = 3.828125
3.515625 + -3.75x + x2 = 3.828125

Factor a perfect square on the left side:
(x + -1.875)(x + -1.875) = 3.828125

Calculate the square root of the right side: 1.95655948

Break this problem into two subproblems by setting 
(x + -1.875) equal to 1.95655948 and -1.95655948.

Subproblem 1

x + -1.875 = 1.95655948 Simplifying x + -1.875 = 1.95655948 Reorder the terms: -1.875 + x = 1.95655948 Solving -1.875 + x = 1.95655948 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = 1.95655948 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = 1.95655948 + 1.875 x = 1.95655948 + 1.875 Combine like terms: 1.95655948 + 1.875 = 3.83155948 x = 3.83155948 Simplifying x = 3.83155948

Subproblem 2

x + -1.875 = -1.95655948 Simplifying x + -1.875 = -1.95655948 Reorder the terms: -1.875 + x = -1.95655948 Solving -1.875 + x = -1.95655948 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = -1.95655948 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = -1.95655948 + 1.875 x = -1.95655948 + 1.875 Combine like terms: -1.95655948 + 1.875 = -0.08155948 x = -0.08155948 Simplifying x = -0.08155948

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.83155948, -0.08155948}

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