1.6=-16x^2+64x

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Solution for 1.6=-16x^2+64x equation:


Simplifying
1.6 = -16x2 + 64x

Reorder the terms:
1.6 = 64x + -16x2

Solving
1.6 = 64x + -16x2

Solving for variable 'x'.

Reorder the terms:
1.6 + -64x + 16x2 = 64x + -64x + -16x2 + 16x2

Combine like terms: 64x + -64x = 0
1.6 + -64x + 16x2 = 0 + -16x2 + 16x2
1.6 + -64x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
1.6 + -64x + 16x2 = 0

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

Divide each side by '16'.
0.1 + -4x + x2 = 0

Move the constant term to the right:

Add '-0.1' to each side of the equation.
0.1 + -4x + -0.1 + x2 = 0 + -0.1

Reorder the terms:
0.1 + -0.1 + -4x + x2 = 0 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + -4x + x2 = 0 + -0.1
-4x + x2 = 0 + -0.1

Combine like terms: 0 + -0.1 = -0.1
-4x + x2 = -0.1

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 = -0.1 + 4

Reorder the terms:
4 + -4x + x2 = -0.1 + 4

Combine like terms: -0.1 + 4 = 3.9
4 + -4x + x2 = 3.9

Factor a perfect square on the left side:
(x + -2)(x + -2) = 3.9

Calculate the square root of the right side: 1.974841766

Break this problem into two subproblems by setting 
(x + -2) equal to 1.974841766 and -1.974841766.

Subproblem 1

x + -2 = 1.974841766 Simplifying x + -2 = 1.974841766 Reorder the terms: -2 + x = 1.974841766 Solving -2 + x = 1.974841766 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 = 1.974841766 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.974841766 + 2 x = 1.974841766 + 2 Combine like terms: 1.974841766 + 2 = 3.974841766 x = 3.974841766 Simplifying x = 3.974841766

Subproblem 2

x + -2 = -1.974841766 Simplifying x + -2 = -1.974841766 Reorder the terms: -2 + x = -1.974841766 Solving -2 + x = -1.974841766 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 = -1.974841766 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.974841766 + 2 x = -1.974841766 + 2 Combine like terms: -1.974841766 + 2 = 0.025158234 x = 0.025158234 Simplifying x = 0.025158234

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.974841766, 0.025158234}

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