x=20-16x^2+32x

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Solution for x=20-16x^2+32x equation:


Simplifying
x = 20 + -16x2 + 32x

Reorder the terms:
x = 20 + 32x + -16x2

Solving
x = 20 + 32x + -16x2

Solving for variable 'x'.

Reorder the terms:
-20 + x + -32x + 16x2 = 20 + 32x + -16x2 + -20 + -32x + 16x2

Combine like terms: x + -32x = -31x
-20 + -31x + 16x2 = 20 + 32x + -16x2 + -20 + -32x + 16x2

Reorder the terms:
-20 + -31x + 16x2 = 20 + -20 + 32x + -32x + -16x2 + 16x2

Combine like terms: 20 + -20 = 0
-20 + -31x + 16x2 = 0 + 32x + -32x + -16x2 + 16x2
-20 + -31x + 16x2 = 32x + -32x + -16x2 + 16x2

Combine like terms: 32x + -32x = 0
-20 + -31x + 16x2 = 0 + -16x2 + 16x2
-20 + -31x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
-20 + -31x + 16x2 = 0

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

Divide each side by '16'.
-1.25 + -1.9375x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -1.9375x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -1.9375x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -1.9375x + x2 = 0 + 1.25
-1.9375x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-1.9375x + x2 = 1.25

The x term is -1.9375x.  Take half its coefficient (-0.96875).
Square it (0.9384765625) and add it to both sides.

Add '0.9384765625' to each side of the equation.
-1.9375x + 0.9384765625 + x2 = 1.25 + 0.9384765625

Reorder the terms:
0.9384765625 + -1.9375x + x2 = 1.25 + 0.9384765625

Combine like terms: 1.25 + 0.9384765625 = 2.1884765625
0.9384765625 + -1.9375x + x2 = 2.1884765625

Factor a perfect square on the left side:
(x + -0.96875)(x + -0.96875) = 2.1884765625

Calculate the square root of the right side: 1.479350047

Break this problem into two subproblems by setting 
(x + -0.96875) equal to 1.479350047 and -1.479350047.

Subproblem 1

x + -0.96875 = 1.479350047 Simplifying x + -0.96875 = 1.479350047 Reorder the terms: -0.96875 + x = 1.479350047 Solving -0.96875 + x = 1.479350047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.96875' to each side of the equation. -0.96875 + 0.96875 + x = 1.479350047 + 0.96875 Combine like terms: -0.96875 + 0.96875 = 0.00000 0.00000 + x = 1.479350047 + 0.96875 x = 1.479350047 + 0.96875 Combine like terms: 1.479350047 + 0.96875 = 2.448100047 x = 2.448100047 Simplifying x = 2.448100047

Subproblem 2

x + -0.96875 = -1.479350047 Simplifying x + -0.96875 = -1.479350047 Reorder the terms: -0.96875 + x = -1.479350047 Solving -0.96875 + x = -1.479350047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.96875' to each side of the equation. -0.96875 + 0.96875 + x = -1.479350047 + 0.96875 Combine like terms: -0.96875 + 0.96875 = 0.00000 0.00000 + x = -1.479350047 + 0.96875 x = -1.479350047 + 0.96875 Combine like terms: -1.479350047 + 0.96875 = -0.510600047 x = -0.510600047 Simplifying x = -0.510600047

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.448100047, -0.510600047}

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