0=-16x^2+64x+5

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Solution for 0=-16x^2+64x+5 equation:


Simplifying
0 = -16x2 + 64x + 5

Reorder the terms:
0 = 5 + 64x + -16x2

Solving
0 = 5 + 64x + -16x2

Solving for variable 'x'.

Combine like terms: 0 + -5 = -5
-5 + -64x + 16x2 = 5 + 64x + -16x2 + -5 + -64x + 16x2

Reorder the terms:
-5 + -64x + 16x2 = 5 + -5 + 64x + -64x + -16x2 + 16x2

Combine like terms: 5 + -5 = 0
-5 + -64x + 16x2 = 0 + 64x + -64x + -16x2 + 16x2
-5 + -64x + 16x2 = 64x + -64x + -16x2 + 16x2

Combine like terms: 64x + -64x = 0
-5 + -64x + 16x2 = 0 + -16x2 + 16x2
-5 + -64x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
-5 + -64x + 16x2 = 0

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

Divide each side by '16'.
-0.3125 + -4x + x2 = 0

Move the constant term to the right:

Add '0.3125' to each side of the equation.
-0.3125 + -4x + 0.3125 + x2 = 0 + 0.3125

Reorder the terms:
-0.3125 + 0.3125 + -4x + x2 = 0 + 0.3125

Combine like terms: -0.3125 + 0.3125 = 0.0000
0.0000 + -4x + x2 = 0 + 0.3125
-4x + x2 = 0 + 0.3125

Combine like terms: 0 + 0.3125 = 0.3125
-4x + x2 = 0.3125

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 0.3125 + 4

Reorder the terms:
4 + -4x + x2 = 0.3125 + 4

Combine like terms: 0.3125 + 4 = 4.3125
4 + -4x + x2 = 4.3125

Factor a perfect square on the left side:
(x + -2)(x + -2) = 4.3125

Calculate the square root of the right side: 2.076655966

Break this problem into two subproblems by setting 
(x + -2) equal to 2.076655966 and -2.076655966.

Subproblem 1

x + -2 = 2.076655966 Simplifying x + -2 = 2.076655966 Reorder the terms: -2 + x = 2.076655966 Solving -2 + x = 2.076655966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 2.076655966 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.076655966 + 2 x = 2.076655966 + 2 Combine like terms: 2.076655966 + 2 = 4.076655966 x = 4.076655966 Simplifying x = 4.076655966

Subproblem 2

x + -2 = -2.076655966 Simplifying x + -2 = -2.076655966 Reorder the terms: -2 + x = -2.076655966 Solving -2 + x = -2.076655966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -2.076655966 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.076655966 + 2 x = -2.076655966 + 2 Combine like terms: -2.076655966 + 2 = -0.076655966 x = -0.076655966 Simplifying x = -0.076655966

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.076655966, -0.076655966}

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