x^2+8x-20=16x-3

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Solution for x^2+8x-20=16x-3 equation:


Simplifying
x2 + 8x + -20 = 16x + -3

Reorder the terms:
-20 + 8x + x2 = 16x + -3

Reorder the terms:
-20 + 8x + x2 = -3 + 16x

Solving
-20 + 8x + x2 = -3 + 16x

Solving for variable 'x'.

Reorder the terms:
-20 + 3 + 8x + -16x + x2 = -3 + 16x + 3 + -16x

Combine like terms: -20 + 3 = -17
-17 + 8x + -16x + x2 = -3 + 16x + 3 + -16x

Combine like terms: 8x + -16x = -8x
-17 + -8x + x2 = -3 + 16x + 3 + -16x

Reorder the terms:
-17 + -8x + x2 = -3 + 3 + 16x + -16x

Combine like terms: -3 + 3 = 0
-17 + -8x + x2 = 0 + 16x + -16x
-17 + -8x + x2 = 16x + -16x

Combine like terms: 16x + -16x = 0
-17 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + -8x + 17 + x2 = 0 + 17

Reorder the terms:
-17 + 17 + -8x + x2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -8x + x2 = 0 + 17
-8x + x2 = 0 + 17

Combine like terms: 0 + 17 = 17
-8x + x2 = 17

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 17 + 16

Reorder the terms:
16 + -8x + x2 = 17 + 16

Combine like terms: 17 + 16 = 33
16 + -8x + x2 = 33

Factor a perfect square on the left side:
(x + -4)(x + -4) = 33

Calculate the square root of the right side: 5.744562647

Break this problem into two subproblems by setting 
(x + -4) equal to 5.744562647 and -5.744562647.

Subproblem 1

x + -4 = 5.744562647 Simplifying x + -4 = 5.744562647 Reorder the terms: -4 + x = 5.744562647 Solving -4 + x = 5.744562647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 5.744562647 + 4 Combine like terms: -4 + 4 = 0 0 + x = 5.744562647 + 4 x = 5.744562647 + 4 Combine like terms: 5.744562647 + 4 = 9.744562647 x = 9.744562647 Simplifying x = 9.744562647

Subproblem 2

x + -4 = -5.744562647 Simplifying x + -4 = -5.744562647 Reorder the terms: -4 + x = -5.744562647 Solving -4 + x = -5.744562647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -5.744562647 + 4 Combine like terms: -4 + 4 = 0 0 + x = -5.744562647 + 4 x = -5.744562647 + 4 Combine like terms: -5.744562647 + 4 = -1.744562647 x = -1.744562647 Simplifying x = -1.744562647

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.744562647, -1.744562647}

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