What is the answer to x^2-x+5=(x-a)^2+b ?

The answer to x^2-x+5=(x-a)^2+b is x=(a^2+b-5)/(2a-1);\quad a\ne 1/2

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x^2-x+5=(x-a)^2+b

x^{2} - x + 5 = (x - a)^{2} + b

x = \frac{a ^{2} + b - 5}{2 a - 1}; a \neq = \frac{1}{2}

Solution steps

x^{2} - x + 5 = (x - a)^{2} + b

Expand

(x - a)^{2} + b : x^{2} - 2 a x + a^{2} + b

x^{2} - x + 5 = x^{2} - 2 a x + a^{2} + b

Move

5

to the right side

x^{2} - x = x^{2} - 2 a x + a^{2} + b - 5

Subtract

x^{2} - 2 a x

from both sides

x^{2} - x - (x^{2} - 2 a x) = x^{2} - 2 a x + a^{2} + b - 5 - (x^{2} - 2 a x)

Simplify

2 a x - x = a^{2} + b - 5

Factor

2 a x - x : x (2 a - 1)

x (2 a - 1) = a^{2} + b - 5

Divide both sides by

2 a - 1; a \neq = \frac{1}{2}

x = \frac{a ^{2} + b - 5}{2 a - 1}; a \neq = \frac{1}{2}

f (- 1) 3 x - 1 = - 3

\frac{x}{5 + 11} = \frac{7}{5}

x, y + x = y - 2 - (\frac{( y - 2 )}{3})

x, - x + 3 y = 49

t, s_{t} (t) (t) = f (p_{t} (t) (t) - 1)

What is the answer to x^2-x+5=(x-a)^2+b ?
The answer to x^2-x+5=(x-a)^2+b is x=(a^2+b-5)/(2a-1);\quad a\ne 1/2