What are the solutions to the equation x^2-2ax=b ?

The solutions to the equation x^2-2ax=b are x=a+sqrt(a^2+b),x=a-sqrt(a^2+b)

Find the zeros of x^2-2ax=b

The zeros of x^2-2ax=b are x=a+sqrt(a^2+b),x=a-sqrt(a^2+b)

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x^{2} - 2 a x = b

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

Solution steps

x^{2} - 2 a x = b

Move

b

to the left side

x^{2} - 2 a x - b = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 2 a ) \pm ( - 2 a ) ^{2} - 4 \cdot 1 \cdot ( - b )}{2 \cdot 1}

Simplify

(- 2 a)^{2} - 4 \cdot 1 \cdot (- b) : 2 a^{2} + b

x_{1, 2} = \frac{- ( - 2 a ) \pm 2 a ^{2} + b}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 2 a ) + 2 a ^{2} + b}{2 \cdot 1}, x_{2} = \frac{- ( - 2 a ) - 2 a ^{2} + b}{2 \cdot 1}

x = \frac{- ( - 2 a ) + 2 a ^{2} + b}{2 \cdot 1} : a + a^{2} + b

x = \frac{- ( - 2 a ) - 2 a ^{2} + b}{2 \cdot 1} : a - a^{2} + b

The solutions to the quadratic equation are:

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

x, x^{2} + x^{2} y^{2} + y^{3} = 3

3 x^{2} - 14 x = - 15

250000 = - 425 x^{2} + 45500 x - 650000

2 y^{2} + 10 = 42

25 - \frac{1}{4} x - \frac{1}{2} = - \frac{3}{4} x^{2} + 25

What are the solutions to the equation x^2-2ax=b ?
The solutions to the equation x^2-2ax=b are x=a+sqrt(a^2+b),x=a-sqrt(a^2+b)
Find the zeros of x^2-2ax=b
The zeros of x^2-2ax=b are x=a+sqrt(a^2+b),x=a-sqrt(a^2+b)