54=-.8x^2+64x

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Solution for 54=-.8x^2+64x equation:


Simplifying
54 = -0.8x2 + 64x

Reorder the terms:
54 = 64x + -0.8x2

Solving
54 = 64x + -0.8x2

Solving for variable 'x'.

Reorder the terms:
54 + -64x + 0.8x2 = 64x + -64x + -0.8x2 + 0.8x2

Combine like terms: 64x + -64x = 0
54 + -64x + 0.8x2 = 0 + -0.8x2 + 0.8x2
54 + -64x + 0.8x2 = -0.8x2 + 0.8x2

Combine like terms: -0.8x2 + 0.8x2 = 0.0
54 + -64x + 0.8x2 = 0.0

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

Divide each side by '0.8'.
67.5 + -80x + x2 = 0

Move the constant term to the right:

Add '-67.5' to each side of the equation.
67.5 + -80x + -67.5 + x2 = 0 + -67.5

Reorder the terms:
67.5 + -67.5 + -80x + x2 = 0 + -67.5

Combine like terms: 67.5 + -67.5 = 0.0
0.0 + -80x + x2 = 0 + -67.5
-80x + x2 = 0 + -67.5

Combine like terms: 0 + -67.5 = -67.5
-80x + x2 = -67.5

The x term is -80x.  Take half its coefficient (-40).
Square it (1600) and add it to both sides.

Add '1600' to each side of the equation.
-80x + 1600 + x2 = -67.5 + 1600

Reorder the terms:
1600 + -80x + x2 = -67.5 + 1600

Combine like terms: -67.5 + 1600 = 1532.5
1600 + -80x + x2 = 1532.5

Factor a perfect square on the left side:
(x + -40)(x + -40) = 1532.5

Calculate the square root of the right side: 39.147158262

Break this problem into two subproblems by setting 
(x + -40) equal to 39.147158262 and -39.147158262.

Subproblem 1

x + -40 = 39.147158262 Simplifying x + -40 = 39.147158262 Reorder the terms: -40 + x = 39.147158262 Solving -40 + x = 39.147158262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = 39.147158262 + 40 Combine like terms: -40 + 40 = 0 0 + x = 39.147158262 + 40 x = 39.147158262 + 40 Combine like terms: 39.147158262 + 40 = 79.147158262 x = 79.147158262 Simplifying x = 79.147158262

Subproblem 2

x + -40 = -39.147158262 Simplifying x + -40 = -39.147158262 Reorder the terms: -40 + x = -39.147158262 Solving -40 + x = -39.147158262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = -39.147158262 + 40 Combine like terms: -40 + 40 = 0 0 + x = -39.147158262 + 40 x = -39.147158262 + 40 Combine like terms: -39.147158262 + 40 = 0.852841738 x = 0.852841738 Simplifying x = 0.852841738

Solution

The solution to the problem is based on the solutions from the subproblems. x = {79.147158262, 0.852841738}

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