16x^2-8x+1=-x^2+5

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Solution for 16x^2-8x+1=-x^2+5 equation:


Simplifying
16x2 + -8x + 1 = -1x2 + 5

Reorder the terms:
1 + -8x + 16x2 = -1x2 + 5

Reorder the terms:
1 + -8x + 16x2 = 5 + -1x2

Solving
1 + -8x + 16x2 = 5 + -1x2

Solving for variable 'x'.

Reorder the terms:
1 + -5 + -8x + 16x2 + x2 = 5 + -1x2 + -5 + x2

Combine like terms: 1 + -5 = -4
-4 + -8x + 16x2 + x2 = 5 + -1x2 + -5 + x2

Combine like terms: 16x2 + x2 = 17x2
-4 + -8x + 17x2 = 5 + -1x2 + -5 + x2

Reorder the terms:
-4 + -8x + 17x2 = 5 + -5 + -1x2 + x2

Combine like terms: 5 + -5 = 0
-4 + -8x + 17x2 = 0 + -1x2 + x2
-4 + -8x + 17x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-4 + -8x + 17x2 = 0

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

Divide each side by '17'.
-0.2352941176 + -0.4705882353x + x2 = 0

Move the constant term to the right:

Add '0.2352941176' to each side of the equation.
-0.2352941176 + -0.4705882353x + 0.2352941176 + x2 = 0 + 0.2352941176

Reorder the terms:
-0.2352941176 + 0.2352941176 + -0.4705882353x + x2 = 0 + 0.2352941176

Combine like terms: -0.2352941176 + 0.2352941176 = 0.0000000000
0.0000000000 + -0.4705882353x + x2 = 0 + 0.2352941176
-0.4705882353x + x2 = 0 + 0.2352941176

Combine like terms: 0 + 0.2352941176 = 0.2352941176
-0.4705882353x + x2 = 0.2352941176

The x term is -0.4705882353x.  Take half its coefficient (-0.2352941177).
Square it (0.05536332182) and add it to both sides.

Add '0.05536332182' to each side of the equation.
-0.4705882353x + 0.05536332182 + x2 = 0.2352941176 + 0.05536332182

Reorder the terms:
0.05536332182 + -0.4705882353x + x2 = 0.2352941176 + 0.05536332182

Combine like terms: 0.2352941176 + 0.05536332182 = 0.29065743942
0.05536332182 + -0.4705882353x + x2 = 0.29065743942

Factor a perfect square on the left side:
(x + -0.2352941177)(x + -0.2352941177) = 0.29065743942

Calculate the square root of the right side: 0.539126552

Break this problem into two subproblems by setting 
(x + -0.2352941177) equal to 0.539126552 and -0.539126552.

Subproblem 1

x + -0.2352941177 = 0.539126552 Simplifying x + -0.2352941177 = 0.539126552 Reorder the terms: -0.2352941177 + x = 0.539126552 Solving -0.2352941177 + x = 0.539126552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2352941177' to each side of the equation. -0.2352941177 + 0.2352941177 + x = 0.539126552 + 0.2352941177 Combine like terms: -0.2352941177 + 0.2352941177 = 0.0000000000 0.0000000000 + x = 0.539126552 + 0.2352941177 x = 0.539126552 + 0.2352941177 Combine like terms: 0.539126552 + 0.2352941177 = 0.7744206697 x = 0.7744206697 Simplifying x = 0.7744206697

Subproblem 2

x + -0.2352941177 = -0.539126552 Simplifying x + -0.2352941177 = -0.539126552 Reorder the terms: -0.2352941177 + x = -0.539126552 Solving -0.2352941177 + x = -0.539126552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2352941177' to each side of the equation. -0.2352941177 + 0.2352941177 + x = -0.539126552 + 0.2352941177 Combine like terms: -0.2352941177 + 0.2352941177 = 0.0000000000 0.0000000000 + x = -0.539126552 + 0.2352941177 x = -0.539126552 + 0.2352941177 Combine like terms: -0.539126552 + 0.2352941177 = -0.3038324343 x = -0.3038324343 Simplifying x = -0.3038324343

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.7744206697, -0.3038324343}

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