47=-16x^2-4x+64

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Solution for 47=-16x^2-4x+64 equation:


Simplifying
47 = -16x2 + -4x + 64

Reorder the terms:
47 = 64 + -4x + -16x2

Solving
47 = 64 + -4x + -16x2

Solving for variable 'x'.

Combine like terms: 47 + -64 = -17
-17 + 4x + 16x2 = 64 + -4x + -16x2 + -64 + 4x + 16x2

Reorder the terms:
-17 + 4x + 16x2 = 64 + -64 + -4x + 4x + -16x2 + 16x2

Combine like terms: 64 + -64 = 0
-17 + 4x + 16x2 = 0 + -4x + 4x + -16x2 + 16x2
-17 + 4x + 16x2 = -4x + 4x + -16x2 + 16x2

Combine like terms: -4x + 4x = 0
-17 + 4x + 16x2 = 0 + -16x2 + 16x2
-17 + 4x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
-17 + 4x + 16x2 = 0

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

Divide each side by '16'.
-1.0625 + 0.25x + x2 = 0

Move the constant term to the right:

Add '1.0625' to each side of the equation.
-1.0625 + 0.25x + 1.0625 + x2 = 0 + 1.0625

Reorder the terms:
-1.0625 + 1.0625 + 0.25x + x2 = 0 + 1.0625

Combine like terms: -1.0625 + 1.0625 = 0.0000
0.0000 + 0.25x + x2 = 0 + 1.0625
0.25x + x2 = 0 + 1.0625

Combine like terms: 0 + 1.0625 = 1.0625
0.25x + x2 = 1.0625

The x term is 0.25x.  Take half its coefficient (0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
0.25x + 0.015625 + x2 = 1.0625 + 0.015625

Reorder the terms:
0.015625 + 0.25x + x2 = 1.0625 + 0.015625

Combine like terms: 1.0625 + 0.015625 = 1.078125
0.015625 + 0.25x + x2 = 1.078125

Factor a perfect square on the left side:
(x + 0.125)(x + 0.125) = 1.078125

Calculate the square root of the right side: 1.038327983

Break this problem into two subproblems by setting 
(x + 0.125) equal to 1.038327983 and -1.038327983.

Subproblem 1

x + 0.125 = 1.038327983 Simplifying x + 0.125 = 1.038327983 Reorder the terms: 0.125 + x = 1.038327983 Solving 0.125 + x = 1.038327983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = 1.038327983 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 1.038327983 + -0.125 x = 1.038327983 + -0.125 Combine like terms: 1.038327983 + -0.125 = 0.913327983 x = 0.913327983 Simplifying x = 0.913327983

Subproblem 2

x + 0.125 = -1.038327983 Simplifying x + 0.125 = -1.038327983 Reorder the terms: 0.125 + x = -1.038327983 Solving 0.125 + x = -1.038327983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = -1.038327983 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -1.038327983 + -0.125 x = -1.038327983 + -0.125 Combine like terms: -1.038327983 + -0.125 = -1.163327983 x = -1.163327983 Simplifying x = -1.163327983

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.913327983, -1.163327983}

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